Why didn't Jesus tell them by what authority he did these things?

The chief priests, the scribes and the elders came to him in the temple (11:27) and asked, "By what authority do you do these things? Or who gave you this authority to do these things?" (11:28) (tap authority). Jesus answered with a question: "I will ask you one question. Answer me, and I will tell you by what authority I do these things" (11:29). "The baptism of John—was it from heaven, or from men? Answer me" (11:30) (tap baptism). Mark tells that "They reasoned with themselves" (11:31): "If we should say, ‘From heaven;’ he will say, ‘Why then did you not believe him?’" (11:31), and "If we should say, ‘From men’" (11:32), and Mark adds, "they feared the people, for all held John to really be a prophet" (11:32). "They answered Jesus, “We don’t know.” Jesus said to them, “Neither will I tell you by what authority I do these things.”" (11:33). Mark gives no reason beyond these words. The reader of Mark has met the word before: "he taught them as having authority, and not as the scribes" (1:22), and "the Son of Man has authority on earth to forgive sins" (2:10).