I think you're mistaking an off hand comment with a very specific subtext for a rude/ uncaring comment.

I'd personally, say "Childbirth is painful, but it affects you in a way very different from other severe pain. It's almost as though a different part of of your brain manages it. Even though the pain level is extremely high, your body can cope with it in the vast majority of cases without responding to to it like other similar levels of pain, like going into shock for example."

I'd say "If you found yourself in an emergency, delivering on your bathroom floor, you'd likely make it through, without help, unlike, say, if you chopped off your thumb." Even though the two would be presumably similarly painful and difficult on the body.

Personally, I found having my cervical suture cut horrifically more painful than childbirth, and I think that's where the childbirth pain vs regular pain comes into play. Someone was cutting shit out of my cervix, and my brain freaked the fuck out. "We're dying, aren't we?". Child birth, I wanted that epidural, oh how I did, but a little voice in my brain while I was asking for it was going "Just keep swimming. We're not dying!"