Unpopular opinion, but I think he's being overly dramatic.
"My Fall 2013 Math 1A students were tracked into the next course in the sequence, Math 1B, and it was found that their average grade in Math 1B was 0.17 grade points higher than that of those students who took Math 1A with another instructor."
0.17. Not even a whole point.
Student evaluations don't really count since those are highly subjective. Students tend to hastily mark whatever they want on them because they want to get the evaluations over with as soon as possible. If a professor is somewhat amicable and invests a moderate level of effort into his/her teaching, then it's not hard to score at least a 6 on average on these evaluations (as students would mark either 6 or 7 in such a case).
Anyway, his performance as a lecturer is irrelevant to his argument. There are three criteria that junior faculty are assessed against in order to become tenured at UC Berkeley (or, otherwise, dismissed): teaching quality, reputation and research. Funny how he left out the last bit. He hasn't published anything since 2013.
And the university is probably firing him to hire another professor at a cheaper salary in order to save money, contrary to his belief that the university is firing him because of disagreements with his teaching philosophy. Universities tend to do this to professors who don't have much research potential and don't teach specialized, upper division courses. The UC system is crippled financially, so departments are more inclined to carry out dismissals of non-tenured professors who don't publish much and who solely teach lower division courses. Non-tenured professors can be fired at will. That's just another day in the life of academia.
The part about the micro-managing harasser and treatment of women, staff and lecturers is definitely worrisome, though. But we need to be careful about believing in these implications absolutely because of Coward's state of mind at the moment. He has already blown the quality of his teaching out of proportion.