Putting on my empathy hat here: if someone has done something to hurt you, like infidelity, you likely care about them. That feeling doesn't just turn off when they hurt you, you just get extra feelings that suck because of those feelings.

Attempting to force contrition or at least acknowledgement is a way to try to lessen those feelings. To go from "I care about this person and they hurt me", to "I care about this person, they hurt me, but they said they shouldn't have, or at least admit that they did".

Feelings are more complex than strictly rational. It can be impossible to stop caring about someone even if you now hate them, which means that unfortunately someone you now have an accutely hostile relationship with can be uniquely positioned to alleviate an aspect of your pain.

Given that, the rational (or at least easiest and most straightforward) thing to do is to build the most compelling case you can to hopefully force them to give you relief, or at least get the catharsis of proving to yourself that they're pathological, which is it's own form of closure.

Saying fuck it is obviously preferable, but it might not be the hand everyone is dealt.