
Angel P. answered 06/20/19
Reading Tutor Specializing in Most Reading/Learning Disabilities
Great question! The threat comes from Professor Snape, who is looking for an opportunity to finally get even with Lupin, Black, and even Harry's dad James.
Picture this: Snape is so angry, and has been for so long, and he finally thinks he is in the right. He won't listen to Lupin, up to the point that he binds and silences him. Black wants to help Lupin, so he heads toward Snape. But Snape gets his wand up first. ("With a roar of rage, Black started toward Snape, but Snape pointed his wand straight between Black's eyes.") Snape is the one in control, and here's the chance for a fight he has thought about for years. That is why he threatens, "Give me a reason." He's threatening and taunting Black, begging Black to give Snape any excuse to put some sort of hex on him--any excuse to get even for all those mean pranks that happened years ago. We know he's the one in control of the situation by the next sentence, "Black stopped dead."
We don't know exactly what he is threatening to do. He is at least threatening to bind him or harm him. Because Sirius Black is a wanted criminal, Professor Snape could do just about anything to him and it would be excused as self-defense.