>>716330858To be clearer there's two things on this: A Reversed social link, and a Broken social link.
A Reversed link means that character is pissed off at you. In P3 it's generally from letting relationships decay or dating too many girls at once, where you can't manage their rapidly-decaying attention period due to the jealousy mechanic dropping it every time you hang out with another girl. In Persona 4 this can only happen twice: If you tell Ai to fuck off on numerous points where she's being an ass and if you tell Naoto to go pound sand when she asks for your help with her family mystery puzzle.
A Reversed link doesn't progress anymore and you need to spend a day with that character apologizing to repair it.
A Broken link means the character actively hates you and doesn't want anything to do with you. You have to spend a reconciliation day with a Reversed link and tell them to fuck off instead to get this to happen. A Broken link stays broken, even in NG+, and requires multiple reconciliation days to fix. And a Broken link prevents you from summoning Personas of that Arcana completely.