They have a history together... of him being the biggest dick in the entire class and making her life horrible the entire time they spent together as kids. He only actually develops a sense of empathy when he is forced to understand what her life was like. He's a horrible person who deserved everything he ever experienced.
Had Nishimiya not immediately forgiven him for every horrible thing he did to her and he had to actually work to have a relationship with her it might work better and be more realistic. As it stands, she apparently forgives everyone for everything they do except Yuzuru, because fuck the only person in the world who tried helping her I guess, which leaves the mother and the sister as the only characters I can actually support.
To say that he should never be able to be forgiven for what he's done is a pretty awful thing to say. He understands how awful he was and realises how terrible it was, what more should he have to do? He's sincerely trying his absolute hardest to fix things, and he planned on killing himself after he apologised. His life has been awful for years since, and the minute things look good for him again, her sister ruins it for him. Do you honestly think he should never be allowed to be forgiven, and should suffer for the rest of his life?
Yuzuru may be trying to support her, but in the worst and most terrible way possible. Her terrible behind the back sneakery, lying and interfering with her life is not how she could help. She's overly protective (with good reason however) and doesn't actually care about what her sister wants, she only cares about what she thinks her sister SHOULD want.
And as shown by the flashback in this chapter, she got very angry when Yuzuru was bullied too as a kid. She gets angry when people attack the people she cares about, not herself.
The fact you support her horrific mother is mildly worrying. Unless you mean his mother. I hope so.