I think your friend is very correct, that this particular thing wouldn't seem bad to most people. Plenty of people say "they're not my dad" about a person who has done them and their loved ones harm. If it felt like one small thing that would help you survive, then I'm glad you had it! I don't think it was immature either. In extreme situations we grasp for whatever strategy we can and creating any sort of distance between you and your father in your mind will likely have helped you at the time.
I do want to say though, I really hear you about the anxiety and worry, and the constantly shifting focus of that anxiety. Your childhood, and surviving the presence of violence in your home probably didn't help that feeling which is experienced many of us who struggle with anxiety - the feeling that "something bad" is going to come for us "sooner or later".
There's even an explanation relating to neurochemicals, where our anxious brains experience a stream of chemicals which are supposed to communicate danger, even when there's no danger, and so our body and parts of our brain act like there IS a danger. When our intellectual thinking-mind looks around and recognises that there's no fire, and no wolves and no bears to hide from we start filling in the gaps with whatever we can. The feeling won't go away and we want to solve the problem so we need an explanation. That's where this digging through the archives of our past actions and regrets comes in.
When this happens to me I get really scared and 'stuck' on a particular problem until something lets me breathe.
If I tell someone I'm anxious and they ask "what are you anxious about?" I say, that for me my anxiety doesn't have something that it's 'about'. Sometimes it is just the feeling of anxiety having a field day inside me... and it can help me a lot if I feel less guilty about not solving it.
This is probably not 100% accurate because honestly it's beyond the edges of my understanding of neurobiology and also probably beyond what science can say given the complexity of the brain, but it helps me a little to explain it to myself.
What do you think for yourself? Do you think it's possible that feeling of fear and dread is there on its own? Without a good reason?
"In between two tall mountains there's a place they call lonesome.
Don't see why they call it lonesome.
I'm never lonesome when I go there." Connie Converse - Talkin' Like You