Responses
I agree that would make way more sense if he can tell the truth through writing. I guess you could justify it by saying Jinsol didn't know or trust Saegye yet. All he'd seen was a guy who cheats on tests and lies to take smoke breaks. Not exactly projecting a selfless do-gooder image.
By the time he made Saegye fall for him he also saw Saegye abandon someone he loved to preserve his own safety, too. It was less risky to lie.
If jinsol explained his situation and asked for help..
Then
Saegye would have exchanged his dare for a short period of time..