From The Founding of Christendom by Warren H. Carroll:
The next two days [after Palm Sunday] He went to the Temple. On Monday, April 3, 30 A.D., the preponderance of evidence suggests that for a second time He drove the money-changers and the animal sellers out of the Temple, the circumstances and His words being very similar to those of His first “cleansing of the Temple” at the beginning of His public ministry two Passovers before. It was this that probably prompted the first challenge flung at Him on that day of ultimate verbal battle, Tuesday, April 4, 30 A.D.: “By what authority are you doing these things, or who gave you this authority to do them?” Jesus’ answer was a counter-question: “Was the baptism of John from heaven or from men? Answer me.” His enemies dared not answer, because the people venerated the memory of John the Baptist and would have been furious if their leaders had publicly denied that God had sent John; yet if they admitted that, they could have no reason for continuing to resist Him Whose coming and glory John had proclaimed. Jesus’ response was far from a mere debating trick; it was both an answer in essence to the question He had been asked – for John was sent by God, and John had called upon all to follow Jesus – and at the same time an effective exposure of the hypocrisy and malice of the Pharisees.
After that, it was all-out war between Jesus and His foes.
God bless,
Jay

Q: And why does a Rabbi answer a question with another question?
A: Why shouldn't a Rabbi answer a question with another question?