Interesting to assume people like Tate didn't exist before. They just changed their rhetoric and added "anti-feminist" to their agenda since that's trendy in certain circles now. These people existed already in much greater numbers in the past.

Masculinity is not the centre of the discussion of the left or even feminism, though. It's just what certain people want to make out of it, which is exactly what the quote above is referring to.

Advancing rights for women in general spans a broad spectrum of intersectionality with masculinity just being one fraction of it. You can look up how many feminists are actually talking about masculinity unprompted and you'd be surprised how infrequent it is. It is a certain group of people with an often anti-feminist agenda who try to make it seem as if masculinity was somehow the main hook of feminist discussion.

Most leftists and feminists want emancipation for men as well, with that they mean the emancipation from gender roles for everyone.