Opponents point to the potential for instability that can result from ceding control to computers that can withdraw from the market at will and take away the liquidity they provide in normally functioning markets. What this line of reasoning ignores is that humans do the same, and there is sufficient evidence that liquidity from all sources will retract during extremely volatile periods. It also ignores the larger regulatory landscape such as Basel III that has already forced traditional liquidity providers out of market making by making it expensive to take risk. The new breed of liquidity providers use smarter computers that get out of the way when they smell serious trouble, as one should expect. Should we penalize them for their intelligence?
A good metaphor for understanding the fears is concern about the famous Rumsfeldian "unknown unknowns," the lurking factors we don't know even exist. Markets are complex social systems where we have witnessed manipulations in the past by humans, but computers bring in a new set of fears because of their speed. The data that can be analyzed digitally also enables astute players to detect and exploit fleeting opportunities. Where it gets tricky is when participants create these fleeting opportunities illegally, comfortable with the fact that regulators don't have the capability to detect their behavior. So why not kill the entire HFT ecosystem by making it prohibitively expensive for them to trade frequently via a tax?
It's the wrong solution because a tax does not resolve a thorny definitional problem. While we may charge the Hounslow trader Navinder Singh Surao based on intent to manipulate markets, it is very difficult to provide a definition of manipulation. For example, what number of order cancellations would be considered "excessive?" If you take the view that in fast moving markets an investor must be vigilant and constantly adjust one's risk, placing and canceling orders frequently might be perfectly desirable by a rational agent to protect capital. Is it fair to curtail the ability to adjust risk in real time as new information becomes available? How do we draw the line?