I haven't read the whole thread yet but OP, his behaviour is ABUSIVE. Not 50/50, not partly your fault, not even slightly your fault. You hitting him had NOTHING to do with what happened, it just conveniently gave him something that he could use to make you feel that you deserved to be treated that way.
He created an argument because you said 'no' to him.
He screamed in your face.
He dragged you around by the arm.
You accidentally hit him in the face.
He used this to further terrify you, despite KNOWING that he had hurt and frightened you.
He pushed you onto the sofa and threatened to punch you in the face.
Please, please read this back to yourself. NOTHING that you did, said, or didn't do caused this. He behaved like this because he feels justified in being abusive. Normal men do not do ANY of the above. A normal (non-abusive) man would be horrified that he had frightened you and would be as you were when you accidentally hit him - horrified and apologetic, because that's what people DO when they care about each other.
This is the first time he has behaved like this. The first time. What do you think the next time will be like? Or the next time? You are rightly shaken, upset and angry and so you should be. Your partner has revealed his true self. His real self. THIS is the real him. Not the hearts and flowers guy who no doubt professes his love and talks the talk and 'lets' you go out with your friends. Words are cheap, they mean nothing. It's what people DO that counts and he has shown you exactly who he is and what he thinks of you. If you ignore this, play it down, pretend it didn't happen and are just glad that he has stopped being nasty and be grateful to him for that, you have just entered an abusive relationship.
He has shown quite clearly, not only by what he did at the time but also by what he did and said afterwards that he is ABUSIVE. He was not sorry. You even walked away from him and gave him time to calm down. Anger didn't cause this OP. This is not an anger management problem, it is an abuse problem.
He made it quite clear to you that he is holding you responsible for his abuse and that if he so felt the need that it WILL happen again. He alluded to his physical strength and what he is capable of. Normal men DO NOT say or do things like that.
Yes he said that he was 'sorry' and that he had 'gone too far' and that he would 'never hurt me'. BUT he DID hurt you OP, he knew he was hurting you, emotionally and physically but he did it anyway, but he didn't care!
How you react now will change your life, forever. You have a choice now to either hope he never does it again and carry on, unwilling to let go of the 'nice guy' who never really existed and who will become a more infrequent visitor as time passes, eventually to never be seen again OR you tell him that he has blown it, leave, have a good life free from abuse and be happy again with a GOOD man. A kind man who would never, ever drag you around or threaten to punch you in the face.
He will do this again, I suspect if you carry on in the relationship it won't be too long before it happens again either. People disagree in normal relationships, how long do you think it will be before you disagree with him again?
Please speak to someone in RL, tell your friends, your mum or family. If you brush this under the carpet you have just given him a green light to abuse you. Please get out while you still can.