Just to be clear, the guy was, if I understood correctly, flirting/dating/asking out the silver haired girl, even though he was dating Guk-Hwa?
I didn't get exactly what he did to make her angry (except that he expected to be forgiven for whatever he's done, just like that).
I think the idea is that he's been a shitty long-term boyfriend to dark-haired girl, borrowing lots of money from her and never returning it, and the straw that broke the camel's back was when she found him on a date with silver-haired girl. I don't think it's entirely clear how long he's been seeing silver-haired girl, but it seems relatively recent, and it doesn't seem like she knew he was already in a relationship/had actually proposed to dark-haired girl, so he was basically lying and cheating on her as well.
Dark-haired girl is pissed that he cheated on her, but more than anything, I feel like she's pissed that she wasted so much time, money, and energy on a relationship that she wasn't even enjoying with a guy who she already should have recognised was a scumbag. The fact that he was a cheating scumbag as well is just the icing on the cake, but it took him cheating for her to finally realise how worthless he always was, and that it wasn't all her fault that their relationship had been stuck in a miserable rut.
Boyfriend wants her to forgive him for cheating on her and take him back, but he doesn't understand that she's come to hate being in a relationship with him and is only now expressing anger that she'd been suppressing for a long time. I figure he's the type of character who thinks that, if he can make the cheating issue go away, then everything has to be fine, because he doesn't think she's allowed to be angry at him for things she didn't complain about at the time, or things they fought about but he considers to be settled.
It's kind of silly, but I can definitely relate to the girl. Wasting so much time and money on someone who's just become someone you're only with because you don't want to be lonely is the worst feeling in the world, especially when they turn around and cheat on you. It's hard to get over that kind of betrayal, so in a way it's satisfying to see someone else handle it in a stronger way than I did.
Throughout the story, it's pointed out that Homura does a lot of things for only Madoka's happiness, not anyone else's. Homura also assumes Madoka wouldn't do the same for her out of love, but out of the kindness of her heart. In the end scene, Homura admits these lingering doubtful thoughts ("You are always...like that...because you're kind.") and gets immediately shot down by Madoka telling her it isn't her kindness that would drive her to search for Homura's happiness, but Homura herself.
Basically I am assuming the story was building itself up for this moment and not many people got it because of the confusing thoughts. This is probably a story reinforcing the idea that Madoka reciprocates Homura's love.