IshiMiko

IshiMiko is a het ship between Yu Ishigami and Miko Iino from the Kaguya-sama: Love Is War fandom.

Canon
Yu Ishigami and Miko Iino have been classmates since middle school. With Miko being a Discipline Comittee member and Yu being a rule breaker (mostly as a result of bringing gaming devices or manga to school), the two's relationship initially consists mostly of bickering. Ishigami often mocking Chika Fujiwara while Miko has a high view on her also didn't help them to get along. The conflict was so intense that in one chapter Miyuko Shirogane and Kobachi Osaragi went through the trouble of making them get along. In the end, they concluded the two act as if they were bullying the person they like, which made Ishigami and Iino act more friendly towards each other to subvert this.

However, in spite of not being fond of her strict nature, Ishigami has actually been secretly helping Miko since the middle school. He would often protect her from bullying, such as by removing a derogatory sign stuck on her back. During the elections arc, Ishigami told Shirogane how much he hates it when someone who works hard is laughed at, referencing Miko Iino, which made his friend confront her in a debate in a manner that would make her lose the elections in a much more dignified way. In one chapter, Ishigame tries to protect Miko's embarrassing secret of listening to "Self Confidence Boosting" soundtracks by exposing his own embarrassing taste in music.

Ironically, Miko also helps Ishigami in secret. When he was suspended for beating up Ogino until he wrote an apology, Iino went to the Discipline Committee to appeal to the lift the suspension. She defended that his other actions to keep up with schoolwork from home indicated upstanding student behavior even if he did not write the apology letter. Neither of them are aware of helping each other, as both believe in justice for justice's sake and/or don't want to be praised for helping others as such behavior should be natural.

Chapters 137 and 140 hint at Miko's feelings towards Ishigami changing to romantic after she finds out his kind side when he gives her the photos of the bonfire that she wanted but couldn't attend, along with a heart-shaped lost item. When Tsubame invites both to her Christmas party, Miko seems interested but initially declines due to believing Ishigami would not like her there. She's surprised and visibly touched when he claims otherwise.

Chapter 152 reveals that Yu Ishigami had accidentally caused Miko's right hand to be broken sometime during the Christmas break. Iino doesn't seem to mind this, though. In fact, she appears to enjoy the fact that Ishigami now feeds her as a form of atonement, which is later revealed to have been suggested by her friend, Rei Onodera. Said girl would also sit between Miko and a boy flirting with her during the party, so that Iino could focus on Ishigami instead.

Ishigami and Miko finally get a chapter where they get along after Yu learns Chika's technique of handling Iino by complimenting her. Although it seemingly doesn't work at first, Miko eventually lets Ishigami take a break from writing notes for her to play video games. They bond as she cheers him on and he notices a kinder side of her that he hadn't been aware of.

During the End of Secrets arc, the supporting characters discuss the relationship between the two and compare it with Ishibame. Chika and Rei ship the two, Kaguya and Osaragi ship Ishibame instead, while Shirogane wants to support both. In the following chapter, Miko is shown to suffer from jealousy as a result of Ishigami successfully going on dates with Tsubame. This arc finally confirms that it was Ishigami who had annonymously written an encouraging letter to Iino back in middle school, saying that her efforts will someday be rewarded. When Osaragi asks him about it, Ishigami says he had written it because the bullying would've broken Miko, as well as because he wanted her to feel better.

Fanon
The ship sailed as a result of the ship tease between Yu Ishigami and Miko Iino. Their polar opposite personalities, with Miko being uptight about the rules and Ishigami constantly breaking them by bringing his game consoles or mangas to school, fueled the ship. So did their constant bickering as a result of such, which makes them appear "like an old married couple." What endeared the fans to the two the most was the fact both have been constantly helping each other behind the other's back. Finally, Chapter 137 made a turning point, heavily implying Iino's new romantic feelings for Ishigami, with future chapters further confirming the feelings on her side.

The ship is currently the most popular ship for both characters, as can be seen on voting polls like this. Considering Yu Ishigami is shipped with almost the entire cast, this can be seen as impressive. Ishigami and Iino's Christmas Arc was the most awaited arc at the time.

The ship was initially a fan favorite when it came to both characters for the manga readers. However, for those who have not read the manga, it lost in popularity to Fujigami. With the second season of the anime, the ship became known for anime fans as well, highly increasing its popularity. Its current main ship rival for the manga readers, both in-universe and in real life, is Ishibame.

The popularity of the ship has led to the creation of a non-canon doujin by one of the fans, depicting a scenario where Ishigami and Iino are dating, as well as several other fan comics portraying the two.

Fandom
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Trivia

 * Two of their first chapters mirror each other as in his debut one Ishigami wants to quit the Student Council, being too afraid of Kaguya, while in the other Iino wants to quit the Student Council because of Kaguya and Shirogane's behavior.
 * They appear together on the cover of Volume 16. They also both appear, along with the other main characters, on the cover of Volume 10.