Catching an L means catching a loss. In this sense, you catch an L if you say something stupid or, if you try to sound intelligent but are proved wrong.
1. Sarah says, "Has anyone ever noticed that "Santa" has the same letters as Satan? Isn't that weird? What are your thoughts?"
Cathy responds, "And Santa is also the word for Saint in many languages. And since the figure of Santa Claus is based off SAINT Nicholas, its not surprising. So nice try, but you failed."
In that case, Sarah caught an L because she tried to prove an invalid point.