I've never said that data supercedes lived experience. In fact, I specifically mentioned learning from and listening to those with lived experience as a core way to become educated. I know for a fact that Elle did a series a while back where she invited men to speak about what society has told them about what it means to be a man.

I still don't see any examples of actual hatred of men (which is what misandry means). What I see are all things caused directly by patriarchy. Custody rights come out of the fact that in a patriarchy being a mother is the single most important thing a woman can do or be and so it's assumed by judges (2/3 of whom are men) that children belong with their mother. Underreporting of sexual abuse and violence against men comes straight out of the patriarchal belief that a man should always be strong, tough, and in control of his woman - and that something is wrong with a man who was "allowed" himself to be abused. Farcical depictions in pop culture is a weird trend, but again, most of that is perpetrated by men, who hold the vast majority of jobs in media, both as writers and as producers.

https://tvtropes.org/pmwiki/pmwiki.php/Main/MostWritersAreMale

You are describing societal trends that are not about a hatred of men as a gender. Women don't have enough societal power to be instituting any of this all on their own. Quoting from Elle's story on Identity Politics:

White males make up about 30% of the population in the US, but still hold the vast majority of social and economic power and they are still represented in media as being the normative citizen.

White people and males are the best-represented identity groups on television. White people, for starters, have an 81% “share of screen” — their representation among shows’ top 10 recurring cast members — even though white people make up only 60% of the U.S. population.

Women make up 52% of the U.S. population but appear on TV screens only 38% of the time.

Men speak 70% of all film dialogue

And four in five experts cited in online news are male

This doesn't mean that there aren't a lot of ways that, despite this cultural centrality and privilege that men suffer under this social system, but it's still an incrediby androcentric one. Just as blacks can't be racist against whites (they can be prejudiced) but they don't have the institutional power to be racist, women do not have the institutional or cultural power to be misandric (except in individual instances).