When Izuru first meets Nagito he attempted to kill him with a gun after the latter prepared to do the same to Junko. However, because of Nagito's luck, the bullet pierces his student handbook instead. Nagito appears almost immediately attracted to Izuru and Kazutaka Kodaka has described the scene as similar to a beautiful, elegant dance.
Both Izuru and Nagito joined Ultimate Despair in order to get a better look at the battle between hope and despair. Both of them also helped out with Junko and Monaca Towa's plots, respectively, for the very same reason, with Nagito heavily assisting Monaca with her plans by guiding Komaru to become a symbol of hope, and Izuru being the mastermind of the Killing School Trip.
When the two meet again (both as members of Ultimate Despair) they do not recognize each other, and while Nagito is very excited about Izuru's company, he merely thinks of him as a completely boring person. This was due to the fact that Izuru asked Junko to erase all memories of him, as he would later erase his own memories about Class 77-B.
In the end, after Hajime and Izuru's identities have mixed, Nagito recognizes him as Hajime and calls him by the name (though at first glance he assumed he is Izuru).
The ship already began to sail during Danganronpa 2 era, with the reveal that Izuru Kamukura is an alter ego of Hajime Hinata who already was involved in a ship with Nagito. The fact that Izuru Kamukura has the talents of every Hope's Peak Academy's student ever and as a result is called the "Ultimate Hope" also helped, considering Nagito's obsession with hope.
The scene from Despair Arc's episode 8 in which Izuru steals Nagito's gun and shoots him while Nagito is clearly under impression, all of which shown with more romantic colors, made the ship even more popular than ever, especially since it confimed Nagito's interest in him.
- Considering Izuru possesess the talents of every Hope's Peak Academy's student ever and also as shown in a scene from episode 8 of Despair Arc, they both possess the Ultimate Luck. However, Izuru's luck appears to outmatch Nagito's, as shown when Nagito's gun jams when he attempts to shoot Kamukura.