I thought of a few reasons why, maybe, though only he knows:
1. Maybe he liked the girl a bit and it was having something of hers near him.
2. She said how she collected it with her father and they had fun, and it looks like YooWon did not have a father who was loving or fun...so a sort of vicarious experience?
3. He felt envy at these kids with nice homes, doting parents, who got to go on vacations and trips and have parties, and that represented part of the world he wished he had--to be a kid who collected memories like that.
I think he didn't steal it conciously like yeah man lets steal some sea shells which cost nothing and just are pretty. He liked it how they looked shiny in a nice jar . Kids usually like things like that . Being poor he had never seen anything like . It fascinated him . He liked it and took it just like that . As we have seen he was pretty clueless in the beginning . By the time he understood it was stealing , it was a huge ruckus. Like whole class made a fuss and he never got the moment to tell semi .
The fact that he left abruptly after taking them tells me he knows he was stealing. But still, I think he both got some sort of "magic shell" feeling from them (they push him on to study) and he regrets it (he keeps bringing it up later). Poor baby. He was under so much stress and didn't fit in....he probably just wanted this beautiful shiny thing from this alien world of the "haves" that cheered him up.
Yup that's pretty much it. He left the party also because he was not fitting in. They were having all rich kid talk and truth and dare game which he had no idea about . He probably just took it like that. I've seen my home maid's son do that in our house. Kid was curious so he took the pretty pen . I mean yeah kids do steal but it's not like adult stealing planned and all . They like something and they take it.
I don't think he did cause neither of your three reasons seems to match to me I think he did it cause he was curious to know why the shells were so important and precious though he found out they were ordinary shells nothing out of the world, and he couldn't understand the sentimental valor they have cause he never have has that kind of experience nor with his dad nor with his mom , and I don't think he never felt bad for stealing them, I think this side of YW if my reasoning turns to be true , shows the side of YW that can be easly despise
wait, he stole it?! That was unexpected. Why do you think he did it? I'd like to know your opinions on that, because I have no clue :)