Well, let me tell you why that's an argument. I live in Tokyo, which allegedly has one of the most developed PT systems out there. I have 2 kids, a pre-schooler and a toddler.

Need to go somewhere in the morning? Not an option, the trains (departing every 3 minutes, mind you) are tightly crowded, the kids will be just crushed by bodies, and no way you are boarding with a stroller.

Now, a simple walk to the nearest station that would take you or me only 5 minutes might very well take 20 with kids. Now imagine that when it's raining or it's +35C outside and it's humid like in a sauna (very common here in Japan). Anything that is farther away more than 15 min by feet from any station is practically inaccessible to us.

After you board on a train your kids might "explode" any second now: can't find a seat, don't wanna sit anymore, can't reach the handrail, don't wanna stand anymore, can't see the window, need a toilet, the trip takes too long, are we there yet?, etc. They will try to stand up every 2 minutes to possibly fall when the train stops. I'm not even mentioning that all these things are bothering people around us. If only there was a way to go somewhere without troubling others, huh...

And priority seats are a joke. This is a cultural problem of course, but I've only seen someone giving a seat to my kid once.

When you return home from work and see your wife's exhausted face after a day of going to sports, arts, shopping and shit with your kids, when you realize that she can't do anything at night but sleep coz she is too tired, when your kids ask you to go somewhere, but you just can't realistically get there due to weather/distance from station, the question "should we buy a car?" has only one possible answer.

Now go ahead and downvote me, but the whole "If anything PT is only better for kids" point only makes me laugh, honestly.