Well first of all, the cause of you're boyfriend being pissed off and in general the fact that he turns up late to pick you up etc etc, I think is partly because he feels slightly trapped in that he eis in a a way responsible for you. By this I mean that he has to help take you fromplace to place etc. Now although he may have been happy to do this, but after a while it perhaps started to get in the wayand meant he couldn't do things that he wanted to do or else it interupted the things that he wanted to do. At the same time though he would feel that he couldn't say no to you because he would be letting you down and feel guilty. So because of this he may start to feel frustrated because he can't decide what to do. It is this frustration which I believe is possibly the root of the problem.
So to have any chance of getting back together I think you first of all regain his trust. You need to tell him to be completely honest with you and insure him that you won't be angry when he is honest,you just want to understand how his feelings. If you do this, it will be like a fresh start. After this you need to both agree to be more open about feelings, so for example if he doesn't want to come pick you up then you can discuss it and then maybe this will put an end to him being quietly frustrated with you not understanding why he is acting in a particular way.
I think also that you should apologise, even if you haven't neccessarily done something wrong, because an apology is often all that is needed to make the other person admit they were wrong and it is generally good for clearing the air. By the sounds of it you don't like losing (based upon the fact you said you don't let go of an argument) but in this case I think it would be worth it because it will help regain the trust of someone you've loved for two years.
So in conclusion, don't put too much pressure on him to quickly, take it all slow, try and get him to be more honest, but not in a forceful way and maybe consider apologising, not because you're at fault but because it might revive you're realtionship.
I hope I've been some help, this is a complicated issue, so if I haven't been as helpful as you'd like explain why and I'll try again =)
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