I agree with his experiences, and there would be more to add. For example our baby-friend families usually were connected via my wife (from birth preparation classes for example), so it was a bit harder/more awkward for me to call them up to hang out so that our kids could play together. That's not active discrimination, just stuff that happens.
I wanted to throw some other thought to HN: I've come to the conclusion that we won't see a big surge in "stay-at-home-daddying". I have nothing against it, but ultimately I think the rationale would be "why would I pay my babysitter half of my salary" (which is what a stay at home dad is getting)? It seems to me a mother still has a bigger claim to her children because she invested much more physically, so society will deem it more acceptable if she does the stay-at-home thing, getting paid more than a mere babysitter.
Or will it become feasible in the future to speculate on becoming a stay-at-home dad? For example (extreme to make a point) instead of taking on another career, take classes in cooking and home decoration in the expectation to one day take care of a home? It seems very unlikely to me, although of course there will be (and already are) lots of women who have and want interesting careers. But would they go forth and marry a guy with no skills but home honing?
Please spare me the sexism comments, I want to think rationally about this. (I personally don't care who stays at home). The point is that it is very viable to speculate on becoming a stay at home mother imo.