What is the general rule for showing just one card?

[KSOT]

The last time I was in a card room I flashed someone my ace after they folded. A woman sitting next to me demanded to see my other card cause "it's the rules." I didn't really care so I flipped up my other card for all to see and then mucked both of them.

I was just wondering if she was right or not. If so, what's to stop a player from mucking one card then showing the other?