Matthew 21:27
And they answered Jesus, and said, We cannot tell. And he said unto them, Neither tell I you by what authority I do these things. And they answered Jesus, and said, We cannot tell. And he said unto them, Neither tell I you by what authority I do these things.
The exchange belongs to the account of the journey to Jerusalem culminating in the triumphal entry, and the authority in question is the authority by which He acted in the temple. When challenged over that authority He met the challenge with a counter-question about whether John's baptism was from heaven or of human origin. To affirm a heavenly origin would expose their unbelief and opposition to John, while to call it human would provoke the wrath of the people who held John to be a prophet and threaten the leaders' standing.
Their reply that they were unable to tell was not honest ignorance or uncertainty but hypocritical evasion, refusal to answer honestly, falsehood and pretense contrary to evidence and conviction. It was driven by fear of the consequences of either answer, by self-protection, cowardice and indecision. Admitting a heavenly origin would have exposed their failure to believe John and their inconsistency in denying Jesus as Messiah and Son of God. John had borne witness to Him after seeing divine glory resting upon Him like a dove of burnished gold and hearing the heavenly declaration of sonship, and after identifying Him as God's sacrificial Lamb.
Resistance to John also arose because the moral power of his pure, self-denying life had brought conviction, while his teaching exposed their religious failures and condemned their conduct, so they chose professed doubt rather than acknowledge they were wrong. Healings, raising the dead and other works had already supplied undeniable evidence of divine mission and of God present in Christ. But the leaders wanted a declaration they could twist against Him rather than evidence leading to faith, and their unwillingness to recognize God in those works and in John's witness showed they would not accept His own testimony that He is the Christ.
He therefore declined to state by what authority He acted, leaving their challenge unanswered. In this He let them become entangled in the net they had spread for Him, and turned their challenge back upon them. The leaders were silenced, baffled and disappointed, standing with downcast hostility and daring no further questions. Thereby they exposed cowardice and lost much of the people's respect, while the multitude watching with intense interest was amused to see proud, self-righteous men defeated.
The refusal came not from a desire to humiliate opponents or from gladness at their difficulty. It used their professed ignorance as an opportunity to speak, set before them their true position and add another warning. For those who would not heed John's warning would not heed Christ's words. The surrounding context warns that profession of service to God without fruit in the life is like a pretentious but fruitless fig tree.