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It's a giant Ponzi scheme
In a Ponzi Scheme, the founders persuade investors that they’ll profit. Bitcoin does not make such a guarantee. There is no central entity, just individuals building an economy.

A Ponzi scheme is a zero sum game. In a Ponzi scheme, early adopters can only profit at the expense of late adopters, and the late adopters always lose. Bitcoin can have a win-win outcome. Earlier adopters profit from the rise in value as Bitcoin becomes better understood and in turn demanded by the public at large. All adopters benefit from the usefulness of a reliable and widely-accepted decentralized peer-to-peer currency.

It is also important to note that Satoshi Nakamoto, creator of bitcoin, has never spent a bitcoin (other than giving them away when they were worthless) which we can verify by checking the blockchain.

Finite coins plus lost coins means deflationary spiral
As deflationary forces may apply, economic factors such as hoarding are offset by human factors that may lessen the chances that a Deflationary spiral will occur.

Bitcoin can't work because there is no way to control inflation
Inflation is simply a rise of prices over time, which is generally the result of the devaluing of a currency. This is a function of supply and demand. Given the fact that the supply of bitcoins is fixed at a certain amount, unlike fiat money, the only way for inflation to get out of control is for demand to disappear. Temporary inflation is possible with a rapid adoption of Fractional Reserve Banking but will stabilize once a substantial number of the 21 million "hard" bitcoins are stored as reserves by banks.

Given the fact that Bitcoin is a distributed system of currency, if demand were to decrease to almost nothing, the currency would be doomed anyway.

The key point here is that Bitcoin as a currency can't be inflated by any single person or entity, like a government, as there's no way to increase supply past a certain amount.

Indeed, the most likely scenario, as Bitcoin becomes more popular and demand increases, is for the currency to increase in value, or deflate, until demand stabilizes.

The Bitcoin community consists of anarchist/conspiracy theorist/gold standard 'weenies'
The members of the community vary in their ideological stances. While it may have been started by ideological enthusiasts, Bitcoin now speaks to a large number of regular pragmatic folks, who simply see its potential for reducing the costs and friction of global e-commerce.

Anyone with enough computing power can take over the network
This is true: see Weaknesses#Attacker has a lot of computing power.

That said, as the network grows, it becomes harder and harder for a single entity to do so. Already the Bitcoin network's computing power is quite ahead of the world's fastest supercomputers, together.

What an attacker can do once the network is taken over is quite limited. Under no circumstances could an attacker create counterfeit coins, fake transactions, or take anybody else's money. An attacker's capabilities are limited to taking back their own money that they very recently spent, and preventing other people's transactions from receiving confirmations. Such an attack would be very costly in resources, and for such meager benefits there is little rational economic incentive to do such a thing.

Furthermore, this attack scenario would only be feasible for as long as it was actively underway. As soon as the attack stopped, the network would resume normal operation.

Bitcoin violates governmental regulations
There is no known governmental regulation which disallows the use of Bitcoin.

See also: the "Bitcoin is illegal because it's not legal tender" myth.

Fractional reserve banking is not possible
It is possible. See the main article, Fractional Reserve Banking and Bitcoin

After 21 million coins are mined, no one will generate new blocks
When operating costs can't be covered by the block creation bounty, which will happen some time before the total amount of BTC is reached, miners will earn some profit from transaction fees. However unlike the block reward, there is no coupling between transaction fees and the need for security, so there is less of a guarantee that the amount of mining being performed will be sufficient to maintain the network's security.

Bitcoin has no built-in chargeback mechanism and this is bad
Bitcoin base-layer transactions are final and irreversible by design, but consumer protection can still built into bitcoin in other layers on top. The most practical way of doing this is multisig escrow. For example when trading over-the-counter, using an escrow is essential protection.

It's worth noting that virtually all successful consumer-facing bitcoin businesses do indeed already implement some kind of consumer protection; Routine escrow was used by Localbitcoins, Silk Road and the bitcoin ebay-site Bitmit. Others such as online bitcoin casinos rely on their long-standing reputation, while others such as Coinbase.com rely on the legal and regulatory system.

The bitcoin method of routinely using escrow has benefits over competitors like credit cards. The security of credit cards is not very good which results in higher costs overall and the possibility of payments being reversed for months afterwards. By contrast when bitcoins have been released to the seller from escrow, they cannot be reversed as the coins are truly in the seller's possession. The requirement to use real-life names for credit cards and PayPal also excludes unbanked people and those from countries with less developed financial infrastructure. There are also downsides like bitcoin is not yet as widely accepted as credit cards and is not a front for providing lines of credit.

Quantum computers would break Bitcoin's security
While ECDSA is indeed not secure under quantum computing, quantum computers don't yet exist and probably won't for a while. The DWAVE system often written about in the press is, even if all their claims are true, not a quantum computer of a kind that could be used for cryptography. Bitcoin's security, when used properly with a new address on each transaction, depends on more than just ECDSA: Cryptographic hashes are much stronger than ECDSA under QC.

Bitcoin's security was designed to be upgraded in a forward compatible way and could be upgraded if this were considered an imminent threat (cf. Aggarwal et al. 2017, "Quantum attacks on Bitcoin, and how to protect against them").

See the implications of quantum computers on public key cryptography.

The risk of quantum computers is also there for financial institutions, like banks, because they heavily rely on cryptography when doing transactions.

Bitcoin makes self-sufficient artificial intelligence possible
StorJ, a theorized autonomous agent which utilizes humans to build itself and issues autonomous payments for improvement work done, is not a conscious entity. Whatever AI is possible, is not going to be magically more possible simply because it could incentivize human behaviour with pseudonymous Bitcoin payments.

Bitcoin mining is a waste of energy and harmful for ecology
No more so than the wastefulness of mining gold out of the ground, melting it down and shaping it into bars, and then putting it back underground again. Not to mention the building of big fancy buildings, the waste of energy printing and minting all the various fiat currencies, the transportation thereof in armored cars by no less than two security guards for each who could probably be doing something more productive, etc.

As far as mediums of exchange go, Bitcoin is actually quite economical of resources, compared to others.

Economic Argument 1

Bitcoin mining is a highly competitive, dynamic, almost perfect market. Mining rigs can be set up and dismantled almost anywhere in the world with relative ease. Thus, market forces are constantly pushing mining activity to places and times where the marginal price of electricity is low or zero. These electricity products are cheap for a reason. Often, it’s because the electricity is difficult (and wasteful) to transport, difficult to store, or because there is low demand and high supply. Using electricity in this way is a lot less wasteful than simply plugging a mining rig into the mains indiscriminately.

For example, Iceland produces an excess of cheap electricity from renewable sources, but it has no way of exporting electricity because of its remote location. It is conceivable that at some point in future Bitcoin mining will only be profitable in places like Iceland, and unprofitable in places like central Europe, where electricity comes mostly from nuclear and fossil sources.

Market forces could even push mining into innovative solutions that have an effective electricity consumption of zero. Mining always produces heat equivalent to the energy consumed - for example, 1000 watts of mining equipment produces the same amount of heat as a 1000 watt heating element used in an electric space heater, hot tub, water heater, or similar appliance. Someone already in a willing position to incur the cost of electricity for its heat value alone could run mining equipment specially designed to mine bitcoins while capturing and utilizing the heat produced, without incurring any energy costs beyond what they already intended to spend on heating.

(Note that this is just an example; mining will not always produce heat equivalent to the energy consumed because some energy is inevitably released as electromagnetic radiation, among others.)

Economic Argument 2

When the environmental costs of mining are considered, they need to be weighed up against the benefits. If you question Bitcoin on the grounds that it consumes electricity, then you should also ask questions like this: Will Bitcoin promote economic growth by freeing up trade? Will this speed up the rate of technological innovation? Will this lead to faster development of green technologies? Will Bitcoin enable new, border crossing smart grid technologies? …

Dismissal of Bitcoin because of its costs, while ignoring its benefits, is a dishonest argument. In fact, any environmental argument of this type is dishonest, not just pertaining to Bitcoin. Along similar lines, it could be argued that wind turbines are bad for the environment because making the steel structure consumes energy.

Economic Argument 3

Bitcoin is designed as a deflationary currency. This means that the purchasing power of a bitcoin will generally increase over time, as opposed to fiat currencies that are designed to lose value over time. This in turn will make people more willing to hold on to their bitcoins, rather than use them for consumption. This reduction in consumption will probably contribute to a net reduction in pollution. However, this is a speculative argument that hasn't been proven right or wrong.

Ratio of Capital Costs versus Electrical Costs

The BFL Jalapeno hashes at 5.5 Gh/s using 30W. That device consumes about $40 per year in electricity (using U.S. residential average of about $0.15 per kWh.) But the device costs over $300 including shipping. Thus, just about a quarter of all costs over a two-year useful life goes to electricity. This compares to GPUs where more than 90% of costs over a two-year life went to electricity. Even more efficient designs can be expected in the future.

Shopkeepers can't seriously set prices in bitcoins because of the volatile exchange rate
The assumption is that bitcoins must be sold immediately to cover operating expenses. If the shopkeeper's back-end expenses were transacted in bitcoins as well, then the exchange rate would be irrelevant. Larger adoption of Bitcoin would make prices sticky. Future volatility is expected to decrease, as the size and depth of the market grows.

In the meantime, many merchants simply regularly pull the latest market rates from the exchanges and automatically update the prices on their websites. Also you might be able to buy a put option in order to sell at a fixed rate for a given amount of time. This would protect you from drops in price and simplify your operations for that time period.

Like Flooz and e-gold, bitcoins serve as opportunities for criminals and will be shut down
Visa, MasterCard, PayPal, and cash all serve as opportunities for criminals as well, but society keeps them around due to their recognized net benefit.
Hopefully Bitcoin will grow to the point where no single organization can disrupt the network, or would be better served by helping it.
Terrorists fly aircraft into buildings, but the governments have not yet abolished consumer air travel. Obviously the public good outweighs the possible bad in their opinion.
Criminal law differs between jurisdictions.
Bitcoins will be shut down by the government just like Liberty Dollars were
Liberty Dollars started as a commercial venture to establish an alternative US currency, including physical banknotes and coins, backed by precious metals. This, in and of itself, is not illegal. They were prosecuted under counterfeiting laws because the silver coins allegedly resembled US currency.

Bitcoins do not resemble the currency of the US or of any other nation in any way, shape, or form. The word "dollar" is not attached to them in any way. The "$" symbol is not used in any way.

Bitcoins have no representational similarity whatsoever to US dollars.

Of course, actually 'shutting down' Liberty Dollars was as easy as arresting the head of the company and seizing the offices and the precious metals used as backing. The decentralized Bitcoin, with no leader, no servers, no office, and no tangible asset backing, does not have the same vulnerability.

Bitcoin is not decentralized because the developers can dictate the software's behavior
The Bitcoin protocol was originally defined by Bitcoin's inventor, Satoshi Nakamoto, and this protocol has now been widely accepted as the standard by the community of miners and users.

Though the developers of the original Bitcoin client still exert influence over the Bitcoin community, their power to arbitrarily modify the protocol is very limited. Since the release of Bitcoin v0.3, changes to the protocol have been minor and always in agreement with community consensus.

Protocol modifications, such as increasing the block award from 25 to 50 BTC, are not compatible with clients already running in the network. If the developers were to release a new client that the majority of miners perceives as corrupt, or in violation of the project’s aims, that client would simply not catch on, and the few users who do try to use it would find that their transactions get rejected by the network.

There are also other Bitcoin clients made by other developers that adhere to the Bitcoin protocol. As more developers create alternative clients, less power will lie with the developers of the original Bitcoin client.

Bitcoin is a pyramid scheme
Bitcoin is nearly opposite of a pyramid scheme in a mathematical sense. Because Bitcoins are algorithmically made scarce, no exponential benefit is derived from introducing new users to use of it. There is a quantitative benefit in having additional interest or demand, but this is in no way exponential.

Bitcoin was hacked
In the history of Bitcoin, there has never been an attack on the block chain that resulted in stolen money from a confirmed output. Neither has there ever been a reported theft resulting directly from a vulnerability in the original Bitcoin client, or a vulnerability in the protocol. Bitcoin is secured by standard cryptographic functions. These functions have been peer reviewed by cryptography experts and are considered unlikely to be breakable in the foreseeable future.

It is safe to say that the currency itself has never been 'hacked'. However, several major websites using the currency have been hacked, often resulting in high profile Bitcoin heists. These heists are misreported in some media as hacks on Bitcoin itself. An analogy: just because someone stole US dollars from a supermarket till, doesn’t mean that the US dollar as a currency has been 'hacked'.

Most bitcoin thefts are the result of inadequate wallet security. In response to the wave of thefts in 2011 and 2012, the community has developed risk-mitigating measures such as wallet encryption, support for multiple signatures, offline wallets, paper wallets, and hardware wallets. As these measures gain adoption by merchants and users, the number of thefts drop.