The pairing of Ichigo Kurosaki and Rukia Kuchiki from The manga/anime Bleach by Tite Kubo. Ichigo is human that can see ghosts. Rukia is a shinigami, or death god, and give Ichigo her powers when she cannot continue fighting so that he may save his family. One of the more popular pairings from the series. It's main rival pairing in the series is Ichihime
Alternative use: stubborn or close-minded.
Although many supporters are reasonable and intelligent individuals, as with most religions, there is an extremist group in the mix. Some Ichiruki shippers, feeling threatened by the possibility of Ichihime, began to resent Orihime Inoue's presence in the series. They started Orihime Hate groups, and would assault Ichihime supporters through unprovoked and irrelevant internet comments about how stupid and worthless Orihime is (often slaughtering the English language and grammar rules). Where Ichihime fans would try to reason and peacefully settle the differences between the two groups, Ichiruki fans would respond by insulting their intelligence and denying any possibility of a different opinion on the subject.
Supporters of this can be violent and abusive with their beliefs, and use logic such as "Rukia punched Ichigo. She's hiding her feelings with violence. She must love him." Oddly enough, most of these people do not punch, kick, or physically abuse their partners. They must not love them.
There are many examples of "Ichiruki moments" throughout Bleach.
See that incredibly high number next to the "thumbs down" button? That's because crazy Ichiruki fans will look up both Ichihime and Ichiruki so that they can vote down on anything that opposes their beliefs, while voting up what ever definitions they find acceptable.