I'm very far from a red-pilled anti-feminist but I do think this is a hugely overlooked problem. Perhaps too much of an aside but I was lucky enough to be able to take an extended parental leave when my child was born, being a "stay at home dad" for the best part of a year. It was incredibly hard work, incredibly rewarding but also a real eye opener at how society still doesn't know what to do with a full-time parent…
I get the "are you babysitting today" whenever I take the kids to the grocery store, but only from women. If men say anything, it's usually a joke about a vasectomy. I find both off-putting, but the "babysitting" thing really is odd. It's Saturday! We're buying groceries!
I know this thread is about a different topic but i went to a dad's lunch at my oldest's middle school. The school put on this presentation about how to be a good dad, it was very humiliating. Like it wasn't even about being a good parent it was just about how not to be a terrible parent, interviews where the guy says things like "i'm a good dad because i'm sitting at the table when my kid is eating dinner" or "i'm a good dad because i don't make jokes about my daughter's weight" etc. I was embarrassed to be sitting there and just turned around and talked, and had lunch, with my son which was why i was there to begin with.