The Jewish authorities were angry with the Lord, for having cast out of the temple those who had made it a place of merchandise, and therefore they come up to Him, to question and tempt Him. Where it is said: "And they come again to Jerusalem: and as he was walking in the temple, there come to him the Chief Priests, and the Scribes, and the elders, and say to him, By what authority do you these things? Or who gave you authority to do these things?" As if they had said: "Who are you that do these things? Do you make yourself a doctor, and ordain yourself Chief Priest?" And indeed, when they say, "By what authority do you these things", they doubt its being the power of God, and wish it to be understood that what He did was the devil's work. When they add also, "Who gave you this authority", they evidently deny that He is the Son of God, since they believe that He works miracles, not by His own but by another's power.
The Lord might indeed have confuted the cavils of his tempters by a direct answer, but prudently puts them a question, that they might be condemned either by their silence or their speaking, which is evident from what is added, "And they reasoned with themselves, saying, If we shall say, From heaven; he will say, Why then did you not believe him?"
As if He had said: "He whom you confess to have had his prophecy from heaven bore testimony of Me, and you have heard from him, by what authority I do these things." It goes on: "But if we shall say, Of men; they feared the people." They saw then that whatever they answered, they should fall into a snare; fearing to be stoned, they feared still more the confession of the truth. Wherefore it goes on: "And they answered and said to Jesus, We cannot tell." It is as if Jesus had said: "I will not tell you what I know, since you will not confess what you know."
We must observe that knowledge is hidden from those who seek it, principally for two reasons, namely, when he who seeks for it either has not sufficient capacity to understand what he seeks for, or when through contempt for the truth, or some other reason, he is unworthy of having that for which he seeks opened to him.
On the Gospel of Mark (St. Bede the Venerable)
Explanations on the New Testament (St. Theophylact of Ochrid)