Why was Posha so mad, Lara was the one who was just raped

We don't know what she wrote in that letter, and when they were talking to each other, we didn't hear their words. It is quite possible Lara did not mention the rape (or maybe not) incident in the letter. She didn't expect compassion from Pasha, she was incriminating herself.
To me, it makes perfect sense that Pasha was shocked. He thought she was pure, because that's what she was when they started dating. (Well, they didn't call it dating in Tsarist Russia, but they seemed quite close in their first scene together.) When he gets to know that Lara was having an affair with that Komarovsky guy, even after she had accepted his proposal…he's visibly upset, he starts to get angry but cannot bring himself to hitting Lara…probably because of what Lara was telling him during the time all we heard was bells chiming.

I remember Pasha telling Kamarovsky at the restaurant that he was 26 and had no 'amorous' experience, and that Lara who was sitting beside him was '17, and that speaks for itself.', meaning that her age was proof that she was inexperienced. It was a shock to him, that she had in fact had amorous experience, and that his lack of experience would be a disadvantage when they married. His anger and hurt were also over the fact that, she had not kept herself pure for him as he had for her. He expected that they would learn together after they married.