So he did screw up (having a good excuse for screwing up doesn't mean that you didn't screw up), but because he is the guy that he is he doesn't want to either apologize or explain.
I agree on that, that's Kakashi's character after all.
Well, Rin being a spy would be just a made up excuse from Kishimoto (although I can't say that I dislike the idea of her being a spy all the way from the start, people like Minato and Kakashi should have been able to figure her out).
If Madara or Zetsu had some influence on the matter then, why not tell him? It wouldn't soil Obito's memory of Rin.
Off topic : I find replying to you in english it a little strange xd
Yes he did screw up and he knows it.It was the only time we saw Kakashi crying and he was deeply hurt and suffered by that.
I don't think it was a set up or he wasn't aware what he was doing.Otherwise he wouldn't react like that afterwards.
I think Kishi will give us the no way around it situation.
I believe it was decided for Rin to die (for spy/medical experiments/threat to Konoha reasons) and Kakashi wanted to do it himself rather than letting anybody else do it.
Or maybe Rin asked him to do it to protect something she knew,an ability etc,etc.
Kakashi didn't know about zetsu or Madara.He could have guessed after Obito told him his story with Madara but in that case too I don't think Kakashi will try to ever explain his reasons or excuse himself to Obito.He know it's his mistake he doesn't want to lighten his position.
I believe if Kakashi is going to reveal what happened will be to avert Obito from resurrecting/further helping Madara with his plans.
OT:Yeah I agree,it's a bit strange xd