Why do people say he burnt the clutch?

Enh. Same way you say "blew a fuse". Did the fuse really get blown on or blow up? It just fits. Its a figure of speech in a way. A clutch can be damaged on a car if shifted badly overtime and not treated properly. They know because theyre car savvy and use logic. You hear a click sound when you start a car and that tells you the starter is messed up.