I actually know of this teacher (although I don't know him personally) and a bit about the situation.
Eton masters have tried for a long time to stir debate amongst the boys about views on feminism, about their role as young adults, and to get them to challenge and question traditional male role models which are no longer helpful in today's society.
As I understood it, the video wasn't what the teacher believed, it was a collection of views which were to spark (heated) debate and actually make the pupils think....
I am not sure why he made the video public in the way he did. Eton wanted the video taken down but he refused, I understand (but I am open to correction here) that he felt Eton were dictating rather than allowing free speech and therefore free debate.
He seemed to get sacked (again, others may know better) for disobeying Eton's orders rather than the debate itself. He was cleared by the TRA because he hadn't actually done anything which prevents him from teaching, like being abusive or safeguarding issues etc. Disobeying Eton's edicts aren't a reason for not being able to teach elsewhere as far as I'm aware....