I was recently heads up in a poker game. My opponent bet, and I called. My opponent immediately said nice call and mucked his cards. He then demanded that I show him my hand. I refused because in my opinion as soon as he mucked his cards he was no longer in the hand. If he had held his cards I would have gladly shown him mine but he immediately threw his cards away. Please tell me who was correct in this situation.
You only have to show your hand when you are up against at least one other, still not mucked hand and you want to claim the pot. You never have to show your cards otherwise.
In this case you are the only one eligible for the pot and thus you don't have to show your hand.
It is funny that he demands you to show your hand. The person that made the last aggressive move (bet, raise) has to show his hand first. He didn't, so you certainly don't have to.