This is a very hard way to live. I’m very glad you wrote. The fighting does have to stop for you to feel safe in your home. The hard part for you to accept is that you can’t change your dad. Stop trying. He is who he is. He’s not interested in changing. He has theories he is going to hold onto no matter how much you argue with him. For you to keep up the fight only frustrates you and angers him. It elevates your anxiety and probably exhausts you both.
You didn’t indicate what you fight about. I suggest that unless there is real danger (like someone smoking in bed, for example), the fights aren’t worth your energy and distress. Walking away is not an admission of blame. It’s the mature thing to do.
You reported past trauma and an anxiety disorder. You didn’t mention whether you have had any treatment for either. If not, you need and deserve the attention and support of a mental health professional so that you can learn skills for managing the anxiety and for recovery from trauma. If you have had treatment in the past, it would be a good idea to get back to your therapist. The fighting isn’t good for you. At 24, you deserve to have the support you need to be able to launch yourself into an adult life — with a job and a place of your own.
The pandemic makes it more difficult to start therapy, but not impossible. There are therapists who work online. You can also jump-start your personal work by ordering some self-help books on recovering from trauma and dealing with anxiety. There are forums here at Psych Central where laypeople provide each other with guidance and support.
Energy you spend fighting will be much better put to use by focusing on your own healing. Give yourself the attention you deserve.
I wish you well.