I know that this was probably explained somewhere else, but why was Gyatso not the head monk ? I know what you're thinking, that maybe wisdom, and not just skills, had something to do with it, but I think Gyatso seemed wise. Maybe it was because Tashi (and maybe the others) didn't like him, and wouldn't want him to be head, but I'm not so sure. Maybe Gyatso wasn't the greatest airbender around at his time, but then that would make Aang 's statement about him being the greatest airbender of his time false. Again, this was probably answered somewhere else, and if it was, could you let me know in the comments below, thanks!
I always thought that the council decided on a new member from on their respective temple's residents should one die or leave, seeing how loosely things seemed to be done there. I don't think that any of the other head monks outright disliked Gyatso, but they may obviously disapproved of his more fun-filled lessons (or at least with Aang, who, to be fair, was the Avatar and they sensed a great danger approaching), especially Tashi.
What makes you think Gyatso was not a master airbender? Did you not see the CRAP TON of Fire Nation military corpses surrounding him? Who do you think defeated them?