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.
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).