I don't see anything childish about tearing your character sheet up and announcing you're done. If you destroy the sheet, people are less likely to try to cajole you into continuing when you really don't feel like it.
Tearing up the sheet means exactly that. It certainly doesn't imply a tantrum, fit, or other childish behavior in and of itself. Expressing your opinion in a clear, unequivocal manner is not childish.
Correct me if I'm wrong - I don't have the books with me - but if I remember correctly, the 2e explanation of being flayed by the Lady of Pain as described as taking the person's character sheet and ripping it into small bits and pieces while describing that nothing about them remains.