Well milo, I think you’re wise in putting this to bed (at least on AB). As I said in my first answer, none of us can say from your description whose fault caused this incident and certainly none of us can say what a civil court would rule if it was put before one. I think this has been adequately borne out by the variety of answers you received.
The world is littered with incidents such as this where each party is convinced he is right. Insurance companies (and often solicitors) take a pragmatic view and try to minimise their losses and I think you would be well advised to do the same, painful as it may be.
Your original question asked
“Also, can i tell my insurance company I do not want them to pay his damages and I want to be taken/take it to court?”
Yes, you can, and they will be more than pleased to be excused liability. Once you have done so you will be on your own. If it goes to court and if (as I suspect) you are unsuccessful or at least only partly successful, you will have a bill for the damage to your own vehicle, possibly one for the damage to the Third Party’s vehicle, your own legal costs, and your opponents legal costs. And don’t be surprised if between now and then the driver of the other car develops mysterious symptoms of injury such as “whiplash” which caused him dreadful pain and suffering and meant he had to take six months off work. You may find yourself liable to recompense him for all or part of this and the repair bills to the vehicles will pale into insignificance. And you will not be able to turn to your insurers for help. Once they are out, they’re out and will not want to know (especially if the matter has gone to court without their knowledge).
This is precisely why you pay your insurance premiums, to minimise your losses when such incidents occur.