A clincher is the thing that finally settles it. Someone was almost sure, almost ready to agree — then one fact, one price, one goal, or one sentence made their mind up. That was the clincher. In an argument it is the point nobody can answer. In a game it is the score that puts the result beyond doubt. It is informal spoken English, common in news and sport. Though actually, people also say ‘That’s the clincher’ about a small, almost silly detail (‘and it comes in red’), not only about grand proofs. It feels like a last firm press: the matter is now closed.