Its because Seo is deeply suicidal. The only thing keeping him alive for the past 10 years has been his sense of responsibility toward the Revengers who died in the dungeon. He sees fulfilling their wills as the last obligation tying him to life. Once that duty is complete, he believes he can finally die “honorably,” without feeling like he wasted the sacrifices his comrades made for him or abandoned them by choosing death too soon.
Yeah, I thought that the issue could also be that death is the only future he imagined for himself, he sees that future as the ultimate relief, so straying would probably cause him even more anxiety. I can relate there, so I can understand the thought process.
But it also feels like he thinks he's not "allowed" to enjoy life. Like he doesn't deserve to live, and he alone has to die. He's scared of taking interest in the coming events, in the future he saw through the watch, because he knows he might lose sight of achieving suicide. When he says it like that it very much feels like a duty, not a will
Spoiler Alert
There was a situation where it was Kangjin had to kill Domin. Seo was hesitant to tell revengers about Domin's secret ability that would basically give him a second life cause he was afraid they would take it. After hesitating he got his mind altered. Since then he had this subconscious guilt because he believes he killed his best friend.
I could go into more detail but it would spoil a lot.

Can someone explain to me why is Seo so hellbent that he "must" die? Not "want", but "must". Like it's his role or duty as survivor to finish the wills and then off himself. Nobody in the revengers wanted him dead, especially if they went as far as giving him these absurdly specific sidequests to ensure he'd actually live and not let himself go.
Like, why "must" he die.