What a fantastic demonstration of the fact that a statement doesn't have to be false in order to be highly misleading.
"Fake" (i.e. blatantly incorrect) news isn't the main problem in out media landscape. Headlines like this one are, which are technically correct, yet are (usually intentionally) crafted to lead the average reader to a conclusion that can be the exact opposite of what is really happening.
It seems like you're framing gender dynamics as a zero-sum game, where improving the situation of one results in stepbacks the other. I agree that men do face significant struggles in today's society [1], but there are ways to move forward in ways that benefit everyone [2].
[1] Perry, Grayson. The Descent of Man. United Kingdom: Penguin Publishing Group, 2017.
[2] hooks, bell. Feminism is for Everybody: Passionate Politics. United Kingdom: Pluto Press, 2000.
By the way, you failed to address his main point that the US is taking a turn towards authoritarianism, and instead chose to critique a secondary part of his claim. Why is that?