It turns out they're correct. According to a video by Prof Robert Sapolsky (1:03:50) males of monogamous species have a receptor for vasopressin that polygamous species don't. Repeated mating elevates vasopressin sensitivity, which is pleasurable and encourages pair bonding and paternal behavior. When females give birth, and when monogamous males hold their new baby, males experience a massive dump of vasopressin which causes a post-partuition hormonal change and causes them to imprint on that child. Females experience a similar dump of oxytocin in a massively pleasurable dopaminergic reaction that encourages both parents to take care of them. South American monkeys that pair-bond do the same thing in the same way, but non-monogamous monkeys don't do this. At birth your baby is basically altering your consciousness with a giant dose of baby drugs, a long-lasting mind-altering physical experience that people who haven't been dosed with baby drugs might very well have difficulty relating to.
(Although this behavior is well-documented in mammals and primates nobody's done experiments to confirm it with humans, probably because the last thing that a new father or an anxious mother wants to do is get hooked up to a bunch of probes and tubes during their child's birth. Even so, this seems like a plausible and reasonably good explanation for the experience that parents have related to me. It's also possible that some males experience this more than others, since the vasopressin reaction related to monogamy and some men are more monogamous than others. Women too, which might be why women use oxytocin; nature can't have non-monogamous women abandoning their children. Also I'm just a speculating layperson, not someone who knows anything.)
I'm posting this partly because it's interesting to me, and partly because I seem to have a lot of friends and coworkers who have kids or are due in the next few months. I'm not posting this to devalue the experience, but to provide context and explanation for what seems to be a really cool thing. If you're one of my pregnant friends who happens to think of this post while or shortly after giving birth and feel inclined to observe your reactions to the experience I'd be curious to hear your thoughts.