One possible reason could be a misunderstanding. Maybe Annabeth made a decision without consulting Percy, like choosing a quest path that Percy thought was too dangerous. Percy, being protective and having his own ideas about how things should be done, might get mad.
It could be because they have very strong expectations that aren't met. Maybe they were really invested in a certain story or character and were let down.
One idea could be a rengoku fanfic where he trains a new group of young slayers. It could focus on his unique teaching methods and how he instills his values in them.
Tanjiro would be a great character to pair with rengoku. Their different personalities could create an interesting interaction. Tanjiro's kind - hearted nature and rengoku's fiery determination could lead to some great storylines.