The Jewish leaders are not coming with a genuine enquiry about Jesus authority, if they were then they would have answered Jesus' question. They were concerned about their own authority and the potential threat to that. They didn't want Jesus to have authroity over them and they didn't want to lose their authority over others, hence the non-reply to avoid a backlash from the crowds. Concern for their own position would lead them to kill Jesus less than a week later.One day, as Jesus was teaching the people in the temple and preaching the gospel, the chief priests and the scribes with the elders came up and said to him, “Tell us by what authority you do these things, or who it is that gave you this authority.” He answered them, “I also will ask you a question. Now tell me, was the baptism of John from heaven or from man?” And they discussed it with one another, saying, “If we say, ‘From heaven,’ he will say, ‘Why did you not believe him?’ But if we say, ‘From man,’ all the people will stone us to death, for they are convinced that John was a prophet.” So they answered that they did not know where it came from. And Jesus said to them, “Neither will I tell you by what authority I do these things.” (Luke 20:1-8)
The idea of Jesus having authority over us is still highly controversial today. In fact, we don't want anyone to have authority... except us. Concern for our position motivates us and leads us to reject Jesus.
Thankfully, Jesus was willing to give up his own position for us and, because of that, we have his position before the Father.