He's ashamed of you OP.
Could it be clearer?
His mother is catholic, has a prized doctor for a son and most certainly doesn't see a young single mother in her son's future.
Not a chance.
She sees some fellow doctor in his future wife.
He knows that you are an absolute No no to bring home.
Your relationship is going absolutely no where.
He may enjoy spending time with you and while away some time as it suits him, but he knows well that you are not a long term bet.
He wants your child not mentioned because things suit him nice and dandy and he has zero interest in the drama that would ensue if his mother found out.
This is who he is and that is his background.
His mother cleans for him.
He hasn't a notion of upsetting his mummy.
All the while you are showing him how little you respect yourself and your child by being involved with someone who would make you deny your own child.
This relationship is going nowhere.