Yu and Yukino aren't his friends. They are merely his club mates.

That is what he believes, at least. That's why he failed to understand how hurting himself hurt those that care about him in the process. Hachiman is used to the abuse and can take it. That does not mean he feels nothing. He just believed that his feelings have lesser value than those of the other people around him, and as such, he sacrificed himself for them.

However, Yui and Yukino clearly think otherwise. They care for him more than they do about the others. Seeing him damage himself with his methods hurt them too. That's why the two of them were so angry at him at the end of the episode.

While I do understand those two, they should also put themselves in Hachiman's shoes. He knows no other way. Just that fact alone implies how horrible a life he has led. It's not like he chose that method because he likes to hurt himself. Despite his cynical thoughts and words, in the end, Hachiman is absurdly kind. That's what those two girls like about him, not his sharp mind.

Scolding him and walking away like that isn't a good way to fix the error of his ways. Hachiman is damaged. Kicking him down more isn't gonna help.