TFA explicitly says that the rise of women is not responsible for the fall of men. I think the point he was trying to make was that, if gender equality was never taken up, the issues facing men today would still be issues facing men today.
For example, the issue of gender balance in tech is widely discussed and taken seriously. The issue of gender balance in prisons is not.
It's not that you can't do both, it's that we haven't, and a primary reason for that is the incumbent political climate, which needs to change.