They asked him where he got his authority. After all, Jesus had not been through the religious training necessary to be among the religious elite.
When pressed, Jesus posed a question to them: Where did John (the baptizer) get his authority, from heaven or from men? This was Jesus's own gotcha question for them. They realized that no matter how they answered, they would bring trouble on themselves.
If they acknowledged that John was inspired by God, Jesus would point out their hypocrisy for not believing him. If they denied he was inspired by God, they thought the crowd would stone them. There was no way to win.
So the teachers of the law just backed down. And got more mad.
There is nothing more maddening than knowing you are wrong and not wanting to admit it.