Please take this answer as purely neutral, I am neiter defending your father nor implying any fault with you. These things are *much* easier to analyze and understand if you remove any trace of the world "fault" from your thinking. Instead, try to find a mindset that mainly revolves around "cause and effect" as the driving motivator.
Also note that this question completely ignores the strangling attack or the getting kicked out, but focuses on the initial events leading up to the rest. I assume that the events before the escalation were simple everyday sister-to-sister bantering, and not some kind of hard abuse.
It went on a bit like that. He just got more and more angry. I kept telling him...
So he went on and on, and you went on and on. It seems to be like both of you wanted to be right at all cost. This kind of discussion can lead to nothing except an escalation.
If anyone of you two had stopped at any time, the situation could and would have defused. Since you obviously cannot make the other person stop in such a situation, you, by pure logic, do have to find a way to stop yourself.
This "stopping" is very, very hard when you are in emotional chaos; especially when you are in a familiar situation. It's like someone is rubbing salt in your wounds. Still, it can be done.
So the takeaway in for this particular part of your situation would be: no, your father does not "always want to be right". You both do, and you have not developed a way to communicate with each other that leads to good results.
What to do
What can I do when my father always wants to be right? How can I speak to him about this?
You do not speak to him about this in the sense of "making him see things".
You shift your own way of thinking and talking. Not because he is your father, but because this is the only thing that ever works in any problematic combination of people. Note that this does not mean that you blame yourself (remember, there is no "fault" involved) or that you just are a passive victim from now on, on the contrary! You are taking hard work on yourself to make your situation better, with the understanding that changing the other person is usually impossible.
Your autism makes it difficult for me to put up specific advice, as I don't know how it manifests in your or your father. I also don't know how your age of 22 translates to your emotional age. But ask yourself a few questions:
- Why were you so emotionally upset by your sisters insults? No, do not write an answer here in the comments, but sit down and really really find out why that is.
- Could you have ignored the insults?
- How did the situation present itself to your father? How is it for him to be a judge between two fighting people?
- Was the initial reaction of your father, patiently explaining something to you, really so bad, considering the spectrum of possible reactions?
- Why was it so hard on you that your father tried to explain something which you already knew?
- What would have been your internal emotional reaction if you had not known what you had done wrong, and your father had explained it?
- What exactly in your reaction could have made your father go nuclear? Was it only the fact that you kept insisting and coming back with the same arguments, time after time?
- You did do something wrong towards your sister (you do not tell us what it was, and it doesn't really matter). Would it have been possible to simply ignore the result, apologize to your sister, and be done with it?
- Was there any way that you could just have said to your father, after letting him explain to you what you did wrong: "Doh, you are right; I thought so myself already. I'm so sorry."? Would that have somehow lessened/weakened you? Would it have solved the situation?
If you give yourself a moment, you probably can think of more questions to ask yourself.
Now, it is perfectly possible and just fine if you can answer only few or even none of those questions. That is a sign that you may benefit from some outside help. This can simply be an outside adult you trust who you can talk to (and ask those or other questions).
Some organizations like the Red Cross or Caritas offer "family therapy", maybe even free. You do not need to drag your father with you, but you can easily go there alone and talk about it with them (make it clear that you want to know what you can do, not what your father can do). It also does not need to take dozens of sessions; maybe one good long talk is enough to get you started.
When and if you get a good understanding in these questions, there may, at a latter date, come a point where you sit down with your father and talk about it in a very relaxed manner, possibly with some neutral moderator. But getting the above questions cleared up for yourself helps a lot, first, and may even resolve the communication problem to some extent.
As said in the preamble, this question only relates to the initial communication problem, not your father trying to strangle you or kick you out of the house.
This is intentional as these are two very different topics. It should be abundantly clear that you do not take physical abuse from anybody. If this subsists, don't fool around with looking for answer, but, plainly, go to the police or stay a few days with friends, relatives or if you really have nobody else, a home for mistreated women or something like that.
There is the (not altogether unlikely) possibility that whatever you or your father do, you will never get these communication issues resolved.
It may be time for you to move out of your parents house. You are an adult, and obviously you do not feel like a small child anymore. Your father now lives with another adult instead of a child, as well.
Try to imagine yourself living on your own, maybe with your boyfriend - does it feel like something you could do?