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.