I usually hate TL;DR comments, but if someone provided a short summary of the argument here (and for bonus points, a critique of the argument's strength), I would be very grateful.
The argument is essentially:
1) High-frequency traders (HFTs) increase liquidity. For the benefit of those who don't know what that means: there are actually a finite amount of shares of each company, and you cannot buy shares unless someone is willing to sell theirs to you, and you cannot sell shares unless someone is willing to buy them from you. You can imagine that you might not be able to sell your shares the instant you want them to if humans are in the loop on the buyer side (i.e., if a human has to review your selling price and decide whether or not to buy), and vice-versa. In contrast, if somebody has programmed a computer to automatically execute trades if certain conditions are met, you can buy and sell shares very quickly. This is what HFTs do.
2) HFTs provide transparent price discovery. This means that the computer programs the HFTs have set up will quickly and unambiguously tell you at what price they are willing to buy and sell shares. Contrast this with a hypothetical process in which you had to haggle with human representatives of each shareholder or potential buyer in order to figure out the price. It's similar to consumer vs. enterprise software sales (sticker price vs. "well, how much can you afford?"). In theory, transparent price discovery promotes fairness (everyone sees the same price) and encourages trading due to decreased latency and hassle.
3) Lots of repetition of 1 and 2. Also an assertion that HFT decreases volatility (average dPrice/dt), while most commentary on the matter assumes that it would increase volatility, due to algorithms that are either busted ( e.g., http://arstechnica.com/business/news/2010/01/how-a-stray-mou...) or interacting with one another in a bad way. It is disconcerting to me that the author cites empirical evidence without a hint of intuition or insight to help the reader generalize it; however, it is difficult to dismiss the evidence off-hand without looking at it more closely and/or being more expert than I in the matter.
Points 1 and 2 are by far the most common and obvious arguments for HFT, and the analysis in TFA is not bad, but not exemplary either. The rest of the article is basically redundant and comes off a little defensive. I found this article interesting ( http://www.zerohedge.com/article/whoa-glitch-hft ), though its tone is also less-than-objective.
The rest of the article seems to make some rather dubious strong claims, also. For example: "High frequency traders can only trade profitably when their trades push a stock price towards fair value."
I don't see why there's any particular reason that's true. High-frequency traders can trade profitably whenever their trades are in line with (very) short-term price movements. Ideally everything works together to push prices towards fair value, but you can't assume that as an axiom, since that's the main point being disputed in that section (the one on volatility).
One other aspect of HFT that was not mentioned in the article is that HFTers often seek arbitrage opportunities. For example, the value of many ETFs such as SPY (i.e. an ETF tracking the S&P 500) are derived from the value of underlying securities. If the value of SPY versus the value of the underlying securities becomes out of sync, HFTers may go long one and short the other and then profit when they converge again. In this sense, HFTers only profit if the market returns to fair value. This applies to many ETFs, convertible securities, and options.
The last section makes an interesting point about the type of speculation that HFT does, i.e. it's not long-term (no positions carried overnight) and thus it can't create the types of asset bubbles that we've seen in the past
