I have decided going homeless maybe better than living with my narc dad

I’m 20 years old. I am currently studying medicine and I still live with my parents. I’ve recently been feeling pretty depressed and overwhelmed and majority of my problems are due to my relationship with my father.

My father is extremely controlling. Even though I’m an adult, I still feel like I have to ask permission to go out. Whenever I tell him I want to go somewhere, I have to answer a 10 page questionnaire and even if he allows he often makes it very obvious that he disapproves like facial expressions, comments, guilt, etc. This is just if I want to go somewhere like a cinema or to a dinner. If I want to go for a night out, it’s just not allowed. He’s pretty religious, so I don’t even bother asking anymore.

Furthermore he also has some very traditional/conservative views. For example, he believes in arranged marriages and that children shouldn’t choose their own partners and shouldn’t really have relationships before marriage. I’m also studying medicine, and when I told him I was considering urology as a specialty, he was not happy because he thinks it’s not appropriate or decent for me to work in that area, especially because I could treat women.

The control doesn't just affect what I’m allowed to do at home. I’m also still dependent on him for transportation since we attend the same university (he is a professor) and usually go and come back together. Even on campus, I don’t feel like I have much privacy. He used to stay in a different area, but recently he’s been spending more time around the library and student areas. He may not be doing it intentionally, but I often feel watched or monitored when he’s around.

I’m 20. I don’t want to spend the next several years asking my father for permission to go out, worrying about whether he approves of my choices, or feeling like I have to justify every decision I make. So I’ve decided that I will not actually give any fuck about him.

For example, instead of asking him if I can go out I will be telling him I am going out and even If he says I can’t go, I will go anyway.

I know this could end very badly like things could escalate significantly. He could become extremely angry or even kick me out and stop supporting me financially as he is paying my tution. And honestly, I’ve mentally reached the point where I’m willing to accept that possibility.

Lastly I think this controlling will never stop if I dont take control now because they have decided what speciality I want to do, where would I go for residency, after completing my residency where would I move for my job e.t.c

Am I approaching this the right way? Is it reasonable at 20 to stop asking for permission and start informing my parents of my plans?