Drinking a hot beverage is much more dangerous than drinking a cold beverage.
Life is full of dangers and risks. Why should birth be any different?
I could post many stories of people who had their first kid in a hospital and had a horrible experience, ends up getting a C section when not really needed, etc (See american C-section rates vs European for example). Then they chose to have a kid at home and had a 100x better experience and a more healthy baby (due to lack of C section and all the problems that leads to).
What you are doing here, is glossing over the underlying logic and falsely reasoning by resemblances. I find this sort of false reasoning flat-out stupid. It needs to be called out so others do not imitate it. (Which is a more meaningful resemblance to anti-vaxxers your comment is exhibiting.)