I like there relationship and the way they nagging each other i just don’t understand wh...

From what I understand, it looks like he ran away from something back in his home area. Prolly why he also stole all the cash. Blow it all, run away from whatever problems that’s dug him into a hole this bad, and call it quits

Well, he made it clear exactly why he wants to end his life. Yang Il-woo feels utterly miserable; before arriving in Gicheon and meeting Bekhee, he never truly felt loved by anyone. He had no family to lean on, nor any trustworthy adults to whom he could confide his feelings. He was completely alone—invisible to the rest of the world. Yang Il-woo has carried this kind of emotional burden since he was very young; while still a minor, he ran away from home, yet neither his aunt nor his cousins cared. They would only call him to tell him to kill himself—caring solely about money, while failing to show even a shred of affection. Aren't those reasons agonizing and soul-crushing enough to make a young man his age want to put an end to his miserable life? The saddest part is that he wanted to do it in a place where no one knew his name—alone, forgotten, and with no one to mourn his passing.

Iirc, he didn't steal that money, it's his, I think his inheritance from his parents. His cousins just think they're entitled to it. And I believe he even left some of it for them. Also, I'm sure he has some other mission in Gicheon, like killing someone, perhaps the person involved in his dad's death, so a murder-suicide.

Ouuuu I didn’t catch the inheritance part, imma need to reread soon to properly understand his story ╥﹏╥