You could go looking for a new therapist, because this one is personally involved, and biased because of it.
It's not offensive to do this, once you explain his bias. In the NL, people who have a personal bias on certain cases will simply be not allowed to deal with them for other patients because it is malpractice.
His own daughter has trans-problems. That creates a bias, and it's usually not easy for parents to deal with it. Completely understandable. I think it's better for both of you if you go your separate ways.
Little edit: I can fully understand some medical professionals do not want to take on trans people. It's nothing discriminating, it seems to me.. Rather; if I were in their shoes, and didn't know all there is to know about such situations, I'd be pretty afraid to screw up. Better have someone do it who does know what they're doing.
I'd choose to get more schooling before I'd start treating trans people.