Board Thread:False Info and Speculative Discussion/@comment-7603754-20160309202205/@comment-26879545-20160402215741

His ability to catch a gun =/= his ability to use a gun.

He'd most likely need to be trained on how to use it, since his father refused to give him a gun when he asked for one before. Either the Sheriff didn't want Stiles to ever touch a gun because he didn't want Stiles to misuse it, or due to some other reason. We don't know the Sheriff's reasons for not letting Stiles use a gun, but if he has a reason, it's possibly safety related.

Braeden threw the gun at Stiles and he was caught off guard; causing him to panic, fumble the gun and then drop it. It was meant for comedic relief, but it was actually a really freakin' stupid thing for Braeden to do, even if it didn't have a clip in it.