He is mixing up "responsibility" with "rights".
Having the responsibility to ensure a child is named, etc, does not automatically mean he has an absolute right to be involved, especially as you are not married, given he will not have PR at birth.
When your child is born, you as the mother get parental responsibility at birth. Assuming you are not married, he only gets PR if he is named on the birth certificate, which can only happen at this point if he comes with you to the registration.
So if he does not attend the registration, he will not have PR, at that point.
However, it will not be difficult in the longer term for him to get it, but of course by that point the child will be named, and any change would require you both to agree, or him to apply to court for a change, at which point the court would make a decision based on the child's best interests.