Toga and Dabi fic, right? It’s interesting because you don't actually get much direct emotional conflict between them in canon. They’re colleagues, they vibe on the same chaotic wavelength. But fanfic writers latch onto the quiet parallels, the ways they're both warped by their upbringings, and build tension from there.
A lot of stories frame Dabi as the more calculated, colder one, while Toga's emotions are volatile and immediate. His conflict becomes about suppressing or dismissing her messy, affectionate advances—seeing her as a liability, a child, or a mirror of his own ruined capacity for connection. Her conflict is the raw hurt of being unwanted, again, by someone whose own scars she thinks she understands.
I've seen fics where the central conflict isn't even verbal arguing; it's Dabi burning a gift she left him, or Toga quietly licking the blood from a cut on his arm while he pointedly stares at the ceiling, refusing to acknowledge the intimacy. The emotion is in what isn't said, in the push-pull between her desperate need to consume love and his rigid refusal to accept it in any form.
The best ones don't try to soften either character. They let Toga be terrifyingly obsessive and Dabi be brutally dismissive, and the tragedy is that their damage aligns just enough to create this awful, magnetic friction. It's less romance and more a study of two broken objects grinding against each other.