Dealing with a Disrespectful Father

I had an argument with my dad yesterday and I'm so frustrated. he texts me at literally 3 in the morning, saying that he "doesn't understand me changing my name". I changed my name to distance myself from my trauma because every time I get called it, I freak out inside and feel sick. he pretty much forced the answer out of me because he was sad that he's "not allowed to know my personal reasonings". he STILL didn't "understand", saying that he "doesn't have any children anymore" because both me and my brother are some kind of trans and changed our names (for different reasons). I told him to stop contacting me while he's drunk or tired, because he CONSTANTLY texts me at 1-3 AM and does some sob story and dumps his problems on me. even my therapist says it's wrong to constantly text me when he's drunk, and then he gets pissed i don't answer him! I told him that I'm tired of it, and to only contact me when he's acting like himself, and he tells me to only contact him "when I'm [deadname] again". ughhhhh im so frustrated I'm literally crying. that was so disrespectful and now I feel bad because my mom told me that i have to "be the bigger person" EVEN THOUGH SHE AGREES WITH ME because he's going through a manic episode because of his BPD. and I feel terrible because I dont want to apologise, I'm really just emotionally exhausted with my dad and what he said was basically a slap to the face, like he was saying that me trying to better myself and be happy is worse than me being how he wants me to be. he didn't even apologise when he sobered up in the morning, just saying that I should "have my speech ready" and stuff. I've muted his contact because my mom told me to, and he's pissed that I'm not responding again. I'm sorry this is so long, I just needed to rant. I don't know what to do. I love him but I can't mentally help him right now and I'm so nervous being around him because of his drinking habits, and I feel like a bad person because even though I really feel like I'm in the right, he's still going through stuff and I can't bring myself to just give in