$\tau$ should be taught in schools
There's plenty of material arguing why $\tau$ is a much more intuitive and easier to teach concept (some of my favorites: 1,2,3) and I don't want to rehash their arguments, but if you think that $\tau$ is just to make equations look nicer, please check out those resources.
The question at hand is whether math educators should teach $\tau$. I will assume that $\tau$ is a more intuitive and didactically nicer concept than $\pi$ for the sake of argument - if you disagree, you can stop reading here.
Many arguments against $\tau$ are appeals to tradition
There seems to be a lot of:
$\pi$ is what we've always used, it is what we currently use, so we should continue using it.
In fact, many of the arguments are generic enough to be able to apply to any proposed change. For example, imagine when the first few countries were switching to the metric system, I'm sure exactly the same arguments were used.
Here is part of EuYu's answer, but with $\tau$ and $\pi$ replaced with "the metric system of units" and "the British system", respectively:
I feel that it is perhaps a little irresponsible to teach the metric system of units instead of British units. As a first introduction, it is the norm which should be taught: teaching a rare alternative to the British units only serves to confuse students, especially when almost all available resources use British units instead of metric units. Imagine a student's confusion when they see meters in class and feet everywhere else.
Some of the arguments for the status-quo have seemed a bit short-sighted. Many changes have a switching cost, but pay perpetual benefits after the switch is over, as in switching to metric units. I think we should be asking ourselves: "Do we really want to be using a didactally and intuively inferior circle constant for the next 500 years?" instead of "Do we want to have to rewrite our textbooks?"
- Yes, textbooks would need to be rewritten, but textbooks get updated all the time with new, modern notation. This is a good thing.
- Yes, "the students would not be able to read older literature" as Markus Klein points out in his answer. True, but when I read a very old journal paper, I already have a hard time. Again, it's because notation changes, usually for the better. I'm glad that people are no longer using the same exact math/physics notation that was used 100 years ago.
Educators can make this change happen
Perhaps more people would agree to switch to $\tau$ if everyone were to do it at once - say, starting in 2015, all professors, all publishers, all researchers, etc. would switch to $\tau$ in one fell swoop. I'm down with that, but that's not going to happen if I've understood human nature correctly.
It has to start somewhere and educators are the gatekeepers of knowledge - educators teach the youngsters and write the textbooks. If the change is going to happen, it will happen thanks to them.
My Personal experience of teaching with $\tau$
I'm the TA for a Math Methods for Physics course at an American univeristy, and I use $\tau$ in my discussions. I wasn't sure how the students would react, but being nimble-minded, young students, they caught on pretty quickly.
I also felt it wasn't a huge burden on any students who were opposed to $\tau$ - I reminded them that they could always just write down "$2\pi$" in their notes every time they see me write "$\tau$". And I reminded them that they were allowed to ask questions using $\pi$ if they preferred (although most of them just asked questions using $\tau$).
Why don't you give $\tau$ a try in your class? See if your students like it. You may find yourself pleasantly surprised with how easily your students become fluent in $\tau$.