When Kokichi cries and appears scared at one point, Angie comforts him by telling him about Atua, the god of the island. Kokichi then appears to calm down immediately, but it's likely that he was just acting and messing with her.
After Angie's student council is formed, Kokichi is shown to dislike it and the brainwashing quite a lot, even having a few genuinely angry reactions as he furiously shouted 'oh come on' when he saw how quickly the students succumbed to brainwashing. More or less jokingly, he proclaimed that the rest of the students should have a war against the student council.
Fans ship the two mostly because of both being the major antagonistic manipulators of V3 cast. Them being a "Foil character" to each other in that regard also helped; with Angie hiding behind passive agressive, cheerful persona and expressing her ideas through her god Atua, and Kokichi being a compulsive liar and hiding behind a villainous persona.
They are also shipped because of Angie comforting Kokichi. However, Kokichi only pretending to be on Angie's side caused many fans to abandon this ship. Kokichi's dislike for Angie's student council made for another reason for people to abandon this ship.
However, because the two rarely interact in canon and because the ship is mostly based on the similarities and differences in their personality and strategy towards the game, it's only a minor ship. It greatly loses in popularity to both characters' main ships, such as Oumasai or Oumota for Kokichi, or Yonameno or Tenkangie for Angie. In spite of being a rather minor ship, it still has a fair number of fanfictions written about them.
- Angie's relationship with Kokichi on Danganronpa Wiki
- Kokichi's relationship with Angie on Danganronpa Wiki