I think after you have touched a piece, you can only abort by resigning the game (or abandoning the board), both of which means losing the game.
Abandoning is a grace given by chess.com; normally, you're committed to a game one you sit down and shake hands.
Here was a game where my opponent didn't wanna play:
http://www.chess.com/livechess/game?id=808156565
Why did he resign? Can't he just abort?