Car Insurance

If you read what happened to me last thursday. I'm very mad a my car insurance which is GEICO.They service is horrible!!They are washing their hands about my car accident saying that the other person is not taking responsability about the accident and there is nothing that they can do about it.So I have to talk to them.Because they don't know their policy and their procedure. My question is So what is their Job? Why I'm paying for every month? If I have to take care of the situation all by my self.I offer them pictures of my car(Geico) and they don't want to see them,"the examinator" didn't say explicity I don't want to see them , he just ignores me everytime that I mention the pictures, and yes I did tell them , so what you guys suppost to do? If I'm taking care of the situation.I want to find reasons why, for their covinience I assume that it will cost them money for any extra..phone calls? and of course if It's my fault It'll go in my records so then they can charge me extra a month.So this is all bussines, I know,I thought that a car insurance will take care of you.We do pay a lot too.If any of you can recommend me a good car insurance I'll really appreciate it.