I am fascinated by this phenomenon. I remember my kid being in a school play when he was young: everybody who wanted could be in it and they clearly added trivial non-speaking spots for kids who might not have passed an audition but still wanted to be on stage. He had one of those! Yet whenever he was on the stage he just dominated -- expanded to fill the whole field of view. At least for me. I really recognized this phenomenon years later when I watched another play which had two kids in its cast who were really good. Probably the first time I really noticed that there were even other kids on the stage.
As for new parents groups: they really are for mothers and aren't about the babies. So I understand what she felt ("It was around the time I abandoned my third or fourth new moms group that I began to consider the possibility that I might be the problem."). And I mean mothers: as a father I was clearly not welcome (this was back in the late 1990s). At the park I was definitely viewed with suspicion by the other mothers even though I was a regular, and none would really talk to me (that's OK, I had EE times and the NYRB). Back then I was the only father pushing a pram around downtown Palo Alto in the middle of the day, and certain segments of the population clearly treated me with scorn. After the 2000 crash I saw more fathers doing this and I hope this has changed to some extent.
Interestingly at a party this phenomenon didn't appear, which I feel was due to context: if I was carrying a baby I believe the presumption was this was a dad being cute and "helping out" and that the rest of the child rearing was done by the mother (in fact she did a lot but had no patience for the American baby rituals). I saw this play out in other countries when I had the baby (and later child).
I don't agree that the child controls the process, but rather the child is a big responsibility, and that controls the process. Frankly owning a home is a lot of responsibility too, but the home is not in control.