This is a really popular headcannon that I've seen different versions of, so here you go:

While George was helping cleaning up after the battle of Hogwarts, he stumbled upon the Mirror of Erised. He had heard legends about it, and was desperate to see what he most desired in life. Staring at the mirror, all he could see was his reflection staring back at him.

Frustrated, he stomped out of the room.

Little did he know, his reflection had two ears and a cheeky grin...