Kurogao's philosophy is painfully simple: you can't change the horrible thing that's happened to you, so there's no point in pretending that anything after that moment can be changed. No matter what you do, you will never be the same person that you were before. So why even bother trying to make a better life?
Ever since Yuri died, Kurogao has devoted himself entirely to revenge. He’s decided that there’s nothing left in his life after this last act of revenge, to the point of revealing his identity to the general public because he doesn’t care about consequences anymore. He’s given up! And now he’s trying to drag Taiyo down to his level.
But Taiyo has already been through that pain. He was the same way after his family died. He didn't have anyone left or anything to live for—his whole life was completely gutted by their deaths. But Mutsumi reached out to him and stayed with him throughout the dark period. Even when Taiyo was actively pushing her away, she didn't leave him. And that’s ultimately what saved Taiyo from withering away in his grief.
Taiyo can empathize with Kurogao because he’s already braved through this issue. Unlike Kurogao, he had people who helped him realize that there IS life after a loss.
Kurogao may not have anything left to live for, but Taiyo sure as hell does. And he’s not going to let Kurogao drag him into the pits of suffering when Mutsumi is waiting for him to come home.