So, I want to come out to my family. My family is supportive, however, my older brother and my biological father are homophobic. They get uncomfortable around gay men because they automatically assume that they want to sleep with them, they think lesbians are a tool for them to "get off" to, and that bisexuality doesn't exist. I do know that the rest of my family would be supportive. My mother has asked me multiple times if I liked girls or not and she told me that she would love me no matter what and I have always told her no because I was still afraid. I'm ready now, but due to my social anxiety, I'm not good with speaking face-to-face with people. How do I get over my anxiety and finally come out of this damn closet?
You've already answered your own question, it seems. You say your mother would be supportive, well, talk to her first. Let it out, bond, and then perhaps discuss where to go from there. Maybe with her help, it'll be easier to come out to whoever you find it necessary to.
If you feel you're ready to come out and don't know how to tell someone face to face, assuming that you want first tell your mother, since she's the most accepting in your family you could write her a letter where you explain everything and what you can't say face to face. Just explain how you feel and why you couldn't say her earlier or why you can't talk about it and I hope everything's gonna be okay. (*hug*)
Tell your mom first. Write her a note if you're too nervous to say it face to face, or just try to get it out quickly whenever you feel brave enough. Once your mom knows she might be able to help you with the rest of your family.
