Well for one thing, he was indeed aiming it at Obito. And also, if you don't know Rin and Kakashi had a thing, she was hot for his balls and all. But it was completely unwarranted. Can you say it's justifiable to be such an *******? Because I can't.
He wasn't aiming at Obito, Obito was the one pissing off Kakashi every time Kakashi pointed out the fact that Obito was breaking a rule
So follow a simple timeline
Obito breaks a rule > Kakashi points it out > Obito insults him > Kakashi owns him
Obito is the one making the first mistake, and considering the condition of Kakashi, it was absolutely normal to react like that
And you spoke of good psychological treatment or something? LMAO Naruto had no support, Sasuke had no support, Kakashi had no support, Kushina had no support
Kakashi had nothing going for Rin as far as we know, he left her to die....