What we caught, we threw away. We kept what we didn't catch. What was it that we kept?

Why this works

This riddle plays with the idea of catching and keeping. When you "catch" lice, you're actually trying to rid yourself of them, so you throw them away. Conversely, what you "keep" are the lice that you didn't catch—meaning the ones that remain on your head. The clever twist lies in understanding that in the context of dealing with lice, catching them is undesirable, while not catching them means they stay with you!