Whenever talking about tau versus pi, the first thing you hear from the pi supporters is appeals to tradition. Luckily, the Pi Manifesto gave mostly mathematical arguments, but even it was affected by fallacious status quo bias in a few places.
First off, whenever it claims that tau is just a multiple of pi, this is only because it defines tau as 2π when it is actually defined as C/r. This argument can easily be turned on pi by saying pi is only important because it is half of tau.
A lot of the quotes are appeals to tradition, especially the last quote in section 1.2. The author of the quote says pi is better just because it has been around since ancient times, but that argument has no logical substance at all and is a perfect example of a logical fallacy called the appeal to tradition. The Babylonians also practiced human sacrifice; why change if now and trash it? Saying we should never change old things is a pretty terrible idea and would result in no progress ever occurring. The part about lemmings is almost as bad as the appeal to tradition; aren't lemmings the ones who just follow along with something just because everyone else is already doing it?
The quote from Siddhartha Gadgil also commits the same fallacy because we would also all be very comfortable with tau, and more comfortable than we are with pi.
The biggest example of status quo bias has to be section 2.3, though. The argument could just as easily be used against pi. Out of 2π, π, π/2, π/4, and 2πi, what makes pi special? Nothing. However, notice that even that list of constants that all have their benefits becomes slightly simpler when written in terms of tau: τ, τ/2, τ/4, τ/8, and τi. Also notice how other than τi, they are all fractions of tau, while with pi, you get some fractions and some multiples.
It's unfortunate that the Pi Manifesto contains these logical fallacies, but overall I applaud the author for staying relatively free of appeals to tradition when compared to many other πist arguments.