Minami didn't know about Kiichirou's family. We have had limited glimpses at it so far so it's hard to give a 100% certain answer (The mom seems abusive). But it's clear that Minami was too infatuated to see the real Kiichirou.
god i know hijiri and kanako are both suffering but godddd. i need someone to save kanako, i'm gonna go read a manga where teenage girls have healthy families, this is getting too realistic to irl