I thought you were going to discuss his sacking. The teacher could have made the video private on youtube and just move on. He was probably trying to make a point and he has the right to do so.
What I found particularly interesting re Eton's reaction to this video is that Eton itself is an institute committed to the development of boys - it's an all-boys fee-paying school. Strange, then, that Eton should seemingly hate masculinity, lol.
Hate masculinity is a strong conclusion. If you were to ask people from different generations what their opinion of what masculinity is, most response will lean on societal ideas of their upbringing and environment. The older you are, the more your views of masculinity will be aligned with woman staying and home and the man being the bread winner. Younger generation will likely not share that point of view.
We have ironed out many wrinkles (in the West, at least, women enjoy the same rights as men) but we can't turn society upside down and expect to thrive.
The above is debatable and it also depends on where you live in the West. The fact that women have certain rights doesn't mean they are allowed to exercise them in the same way as men. Women have the rights to go topless in certain parts of the West but they have to cover their nipples (see the freethenipple movement ). Then you have society call those women whore.