WARNING: The following contains spoilers for Given the Movie, now streaming on Crunchyroll.
One of the brilliant things about Given is its message about the power of music. For people like Mafuyu and Ugetsu, music is the only outlet they have to express what words can't convey. With music, Mafuyu was able to express all of his pain and grief over losing Yuki. It was a powerful tool for him, but we've also seen how music has the power to hurt people, as with Ugetsu and Akihiko in Given the Movie.
Ugetsu and Akihiko met and fell in love because of music, but they're also hurting each other because of it. Their relationship is toxic and the only reason it lasted for two years is that they are scared to let go of each other. Both know they're suffering by staying together, but they can't be without each other. Music was what brought them to each other and it was music that finally allowed the couple to say goodbye.
Akihiko fell in love with Ugetsu after meeting him in high school, where he first heard Ugetsu play. Ugetsu's genius-level talent overwhelmed Akihiko to the point where he quit the violin because he could never be his equal. Somewhere along the way, without knowing it, he began to hate music. There's no denying that Akihiko loves him, but his love was always intertwined with envy, hatred and a desire to destroy. For him, Ugetsu represented his musical failures.
Ugetsu also loves Akihiko -- but he loves music so much more. He feels that his relationship with Akihiko is impeding his freedom to play. Ugetsu isn't emotionless -- although he may act that way -- in fact, every single emotion he feels is augmented, which is why his music has such an ability to resonate. Playing music is his way of feeling. Knowing that the man he loves is suffering because of him and his music, it would be impossible for Ugetsu to ever be free.
Akihiko moves in with Ugetsu shortly before graduation. Ugetsu's room down in the basement has no sunlight and is totally soundproof -- there is nothing except the two of them. It's Ugetsu trying to keep the two things he loves -- music and Akihiko -- all in a contained space, away from the rest of the world. This room was a tether for their relationship and to each other.
Ugetsu didn't react much when Akihiko said he was going to break up, which is understandable given how many times they've broken up and gotten back together again. But he gets scared when Akihiko says that he's going to move out. The room that the two of them were living in together had always been a space of love and hate -- for each other and for music. Even though they'd broken up multiple times, Ugetsu knows that Akihiko would always come back to this room, to him. Hearing his plans to leave makes Ugetsu realize that he might be losing Akihiko...for good.
Both lash out in toxic displays of love and hate, with Ugetsu doing everything he can to hurt Akihiko, waiting for him to be the one to walk away, while also leaving the door open for him to return. Their love for each other is intrinsically tied to the suffering they feel whenever they're together, unable to have one without the other. They run away but then find themselves constantly drawn to each other.
Mafuyu's song "Yoru ga Akeru" was the catalyst for the two of them to finally break up. Just prior to their performance, Akihiko had returned to Ugetsu's house for the first time since he saw him with another lover. But Akihiko's resolve to break up wavered when Ugetsu refused, dropping his drum sticks at the thought of ever truly leaving Ugetsu. But hearing Mafuyu's song reminded him of how much he loved music and who brought that passion back: Haruki.
Ugetsu realized this at the same time. He saw the change in Akihiko, saw his love for music return and he knew that he wasn't the one who did that. Deep down, he knew that the two of them had broken up long ago, but he wasn't ready to face it. And we have to remember that Akihiko was, at least until Mafuyu came, the only person who saw Ugetsu as a human. Ugetsu didn't want to be alone again, especially if it meant losing Akihiko. Akihiko at least had his band and Haruki, while Ugetsu had nothing except his music -- something he'd long resigned himself to. After all, being a prodigy is a lonely existence.
Even though Ugetsu is the one constantly pushing Akihiko away, he's also the one pulling him back in. When he sees Akihiko leaving, for real this time, he can't help but reach out again, despite knowing that they'll end up hurting each other again. And he's just about to call Akihiko back again until he remembers Mafuyu reassuring him that everything will be okay. Mafuyu's song, which translates to "Dawn Breaks," symbolizes the end of a day and the beginning of another, and it's his music that gives Ugetsu the strength to finally let Akihiko go.
