This is probably a terrible place to express my thoughts on this, but I'm going to do it anyway. I've noticed that a lot of people who criticise e.g. feminists, immigrants, religion, gays, and so on, tend to criticise it for things that they often do themselves. For example, feminists are often accused of a culture of victimhood; they "play the victim", when in reality women have very little to complain about. Yet, very often, the same people who do this complain about how straight white men are the most discriminated group of people in the Western world. People often criticise immigrants for being lazy, not having any qualifications, living on benefits, being engaged in drug use and petty crime, and generally being low class scum. But those same people often complain that there no jobs and have had to live off benefits because employers would prefer to hire those lazy, ignorant, drug abusing immigrants instead of native Brits. People who criticise the religious for being dogmatic and not being open to new ideas are often the most dogmatic and close-minded people I've ever had the displeasure of discussing things with. And of course, there are the old jokes about homophobes being closet homosexuals themselves.
So perhaps one reason why some people have joined this backlash against feminism is because they can see in feminists the very things that they hate in themselves. Perhaps, for example, when people shrilly criticise feminists for taking an aggressive, man-hating tone, while simultaneously defending the right to troll people as much as they want on the internet, they are identifying the weaknesses in their own personalities. They are attacking what they hate in themselves, because we are often consciously blind to our own personality defects, but subconsciously acutely aware of them -- and so we project, and see them in other people instead.
Smart people often believe really stupid things because they are incredibly skilled at coming up with rational, logical arguments to support just about anything. Sometimes, unknowingly, our subconscious tells us to believe something, while our conscious invents compelling reasons to support it. Compounding this, we often feel that we know ourselves far better than other people -- when, very often, our friends, family and colleagues can tell us more about our flaws, weaknesses, needs and desires than we know ourselves. We need to be more humble in acknowledging these facts, and critically analyse why we believe what we believe, as if we were our own worst enemy analysing us from the outside. Only then can we really know why we believe the things we believe.