Coming out was the hardest part of my transition. First to my ex, and several years later to my parents, when I was pretty much convinced to start transition. And since my parents are divorced, I had to do it twice. With my mom there was no problem at all, she was understanding and comforting right from the start. But my dad has a weird way of dealing with conflict, he counterattacks with jokes and humor, even if it is completely unfitting. And that was an embarrassing moment for me, I felt ridiculous. He also tried to convince me of leaving all my feelings behind, to try to cope with my dysphoria. But once we had a conversation with the psychologist and he understood everything, he also became fully supportive.
I was just talking about this in group last night, but it frustrates me so much that we still live in a world where many people believe professionals who have only known us for a few hours more than they believe us directly, as experts of our own experience. I'm sorry your Dad reacted like that, that's shit.