There are a few reasons for this.
Firstly, the legal reason why an unmarried father isn't named on the birth certificate if he doesn't attend the appointment is to protect him. Otherwise a woman could name literally any man as the father of her baby, without his knowledge, and he'd have parental responsibility. If he believes he is the father of the baby and he wants parental responsibility, he can get himself added on later.
The mother, on the other hand, is known to be the mother because the hospital notes will confirm that she is the one who gave birth to the baby, and short of giving her baby up for adoption, she doesn't actually get to choose whether she has parental responsibility or not. (But then I suppose the father doesn't get to choose whether she keeps the baby or not, so it's swings and roundabouts there.)
Secondly, if a father has parental responsibility, the mother is greatly restricted in what she can do. She can't move away from where she is living unless her baby's father consents. So if she has moved to be near him, they break up, she has no right to any of her assets or any support from him at all other than meagre child support, but he's on the birth certificate, he can stop her from moving back in with her mum 100 miles away, or moving back to her home town where her family can help with childcare. He can refuse consent to the child receiving recommended vaccinations. He can refuse to let her take the child on holiday. If the mother is from another country and her family live in her home country, he can essentially stop her from taking her child to visit their family. Why should an essentially absent parent have that kind of power?
When you're the one left literally holding the baby, you need to be able to do what works for you and not be dictated to by your child's Disney dad.