Sorry, you don't have kids so you just don't get it. I didn't get it either before I had a kid. All of the reasons you listed, bad public transport, dangerous biking, safety, etc. have nothing to do with why I want to buy an SUV. There are just so many items involved with raising a child. Yes, you might be able to take public transit so your kid can see the doctor, as long as you time it to be at an off-peak time, but there are so many other cases where you need a large car. A very basic example: You have a young child in NYC and you want to spend the weekend with your parents who live in Westchester. Without a kid, getting on Metro North with a small duffel bag of clothes would be trivial. With a kid, you need to bring a crib, toys, stroller, diapers, multiple changes of clothes, and maybe even a high table with you. Good luck getting all of that on the train, especially with a screaming kid!
The failure in your reasoning is that you see parents on the train, so you think that's their only mode of transportation. Yes, you can take the kid on the train for certain errands. Other times, however, having a car is 100x more convenient. And that is true everywhere.