Coming out to therapist

Anyone else find this really hard for someone reason? I'm a 19 year old out closeted gay guy I have told very few people about it. The only people that know about it are a few people online and a guy I have been seeingOne of the main reasons I wanted to go into therapy was to become more comfortable with being gay and eventually be out of the closet ( I guess?). Even though logically coming out to a therapist should be easy I find it really hard. For one thing I don't feel comfortable coming out to a male therapist. Maybe this is internalized homophobia on my part but I feel that the fact that I'm gay would make a lot of guys awkward / uncomfortable. Given the fact that he's a therapist this probly isn't true since I'm sure they see all types of people but I just don't feel comfortable coming out to a straight guy.Today I sort of came out to my therapist that I've been seeing for a while now. It was really hard but I know to make progress in therapy I need to be honest and the fact is I want to talk about it. I ended up saying something along the lines of " I'm afraid of being gay" and then she said well are you gay? And I just said idk. And she said do you like men and again I said idk. I know what you are thinking , this dumb to do this with a therapist. But I can't help but feel even in an environment such as therapy I am still being judged. Some subconscious fear in my mind was thinking " what if she doesn't like gay people".So yea my bad for the rant but if coming out to a therapist is this hard I can't imagine how it is to come out to family and stuff. Even after I told my therapist I felt kinda bad afterwards and still do. The best way to describe it is awkward I guess.