how can you deal with the contradiction between you and your friends?

I just let them think very carefully then they will be the one who realize their own thought. As much as possible, I don't want to get involved in arguments but if I feel I'm getting in to, I just prefer to stay neutral and study very carefully each side.

if it's not my fault,and he/she is in a rage,then i will not keep that calm,maybe i will be more angry.but actually whose fault is it?that's a relative thing.maybe both of us think that 'it's not my fault,it's yours'.i will not be the one to explain things patiently. but,if we are really friends,we do not need to worry about that situation,after a while,we will make up again.by the way,cheating on a friend is unforgivable.

Unless it is a very strict issue and you have to stict to your point, I don't think it's necessary to have a conflict with your friend if he insists his point. Let him have it. It's ok, right? It doesn't hurt you to make a compromise if it is not a serious thing. Otherwise, we have to keep our point and try to persuade him to accept yours if it's important.

I just keep quiet when we have conflicts or explain my side when she is no longer angry. Because if i will also talk at the time she is angry, maybe the anger will still boost more. I don't say SORRY when I know it is not fault. I just wait for her to say sorry but if I know that I was not right, then I will be the first one to say sorry to her....

I'd suggest waiting until she's not so angry anymore, and then talking to her. While I don't think it's necessarily a good thing to apologize for something that you've said if you believe in it, it might be worth apologizing to her for upsetting her, which might even calm her down more and make it possible to talk to her.