I don't really see it that way though. The way I see it the Mc is already cutting himself and hating himself, he has no self love and doesn't care about his wellbeing anymore. He just jumps in the car and walks around aimlessly because he honestly doesn't care what happens to him
That doesn't come into the case, in the first chapter he obviously didn't want to be near the guy, even when he was in the car he said he didn't want to, but contradicts his attitude by staying there and letting himself being pulled around, see? No logical. Other manhwas are like that and they're not suicidal, they're just made that way so the story can flow faster. If he was like you're saying he would never have struggled like in the first chapter.
I wish this manhwa had more logic. Things happening until now get out of nowhere, like they're just there for sake of keep going to next chapter but not logical at all, he just went in a car with a total stranger that seems to know a lot about him and doesn't want to answer who he is, I'm seeing the path like others dumb manhwas were the mc just let everything happen, I hope this one doesn't turn like that.