Intimidation

This is how intimidation usually works.  Someone of in a position of power will make it look like they have a spotless record and that you are doing something wrong, thus making you less likely to stand up to them.  But the fact of the matter is that NOBODY has a spotless record.  They do not have any more right to treat you badly than you have to make a mistake because they are guaranteed to be equally mistake-prone, even if it may not appear that way.

In the case of the chief priests and the elders, they had made a HUGE mistake by refusing to believe the message of John the Baptist.  So they aggressively turned all the attention to the presumed unauthorized teaching in the temple and away from their own unbelief.  Most people would not have dared to call attention to the mistake of the chief priests and elders because their own little errors would have been called out and used against them.  But Jesus is without sin and therefore managed to avoid making any mistakes that could potentially bring Him down.  As a result, He was able to bring attention to what the chief priests and elders did wrong and they did not have an answer for that.  They were exposed for the posers that they were.  Their fortress turned out to be a hollow shell.

Matthew 21: 23-27