OT background text: “God said to Moses, ‘I AM WHO I AM.’ And he said, ‘Say this to the people of Israel, “I AM has sent me to you.”‘” (Exodus 3:14 ESV) … and then, “Jesus said to them, ‘Truly, truly, I say to you, before Abraham was, I am.’ So [the Jewish people listening] picked up stones to throw at him…” (John 8:58-59 ESV).
It’s no wonder the Jews who didn’t accept the testimony of His miracles tried to stone Him to death for saying what you quote above. That was the penalty for blasphemy under the Jewish legal system. It was pretty clear to everyone there He was saying, “I am the God of Israel.”
Mark 14: 60-64 (ESV)
60 The high priest stood up and came forward and questioned Jesus, saying, “Do You not answer? What is it that these men are testifying against You?” 61 But He kept silent and did not answer. Again the high priest was questioning Him, and saying to Him, “Are You the Christ, the Son of the Blessed One?” 62 And Jesus said, “I am; and you shall see the Son of Man sitting at the right hand of Power, and coming with the clouds of heaven.” 63 Tearing his clothes, the high priest *said, “What further need do we have of witnesses? 64 You have heard the blasphemy; how does it seem to you?” And they all condemned Him to be deserving of death.
The Jewish leaders at Jesus’ trial were doubly offended by the above, because not only was He claiming to be God, but He was quoting an obvious reference to the Messiah from Daniel 7 (ESV):
The Son of Man Is Given Dominion
13 “I saw in the night visions, and behold, with the clouds of heaven there came one like a son of man, and he came to the Ancient of Days and was presented before him.
14 And to him was given dominion and glory and a kingdom, that all peoples, nations, and languages should serve him; his dominion is an everlasting dominion, which shall not pass away, and his kingdom one that shall not be destroyed.
C S Lewis’ statement in “Mere Christianity” concerning those who say Jesus is just a good moral teacher, but not the Son of God, is worth noting:
“I am trying here to prevent anyone saying the really foolish thing that people often say about Him: ‘I’m ready to accept Jesus as a great moral teacher, but I don’t accept His claim to be God.’ That is the one thing we must not say. A man who was merely a man and said the sort of things Jesus said would not be a great moral teacher. He would either be a lunatic — on the level with the man who says he is a poached egg — or else he would be the Devil of Hell. You must make your choice. Either this man was, and is, the Son of God: or else a madman or something worse. You can shut Him up for a fool, you can spit at Him and kill Him as a demon; or you can fall at His feet and call Him Lord and God. But let us not come with any patronizing nonsense about His being a great human teacher. He has not left that open to us. He did not intend to.”