Jesus had several interactions with the religious leaders of the Jews. They hated Him because He challenged their authority and often taught contrary to their own teachings. Sometimes, Jesus said things which they thought were simply blasphemous. The passage below is one of these instances.
Then said the Jews unto him, Now we know that thou hast a devil. Abraham is dead, and the prophets; and thou sayest, If a man keep my saying, he shall never taste of death. 53 Art thou greater than our father Abraham, which is dead? and the prophets are dead: whom makest thou thyself? 54 Jesus answered, If I honour myself, my honour is nothing: it is my Father that honoureth me; of whom ye say, that he is your God: 55 Yet ye have not known him; but I know him: and if I should say, I know him not, I shall be a liar like unto you: but I know him, and keep his saying. 56 Your father Abraham rejoiced to see my day: and he saw it, and was glad. 57 Then said the Jews unto him, Thou art not yet fifty years old, and hast thou seen Abraham? 58 Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. 59 Then took they up stones to cast at him: but Jesus hid himself, and went out of the temple, going through the midst of them, and so passed by. (John 8:52-59)
To understand what made the Jews so angry that they wanted to stone Jesus, we need to look to the Hebrew Scriptures (the Old Testament). When Moses was called by God to lead the Israelites out of Egypt, Moses basically asked God who He was.
And Moses said unto God, Behold, when I come unto the children of Israel, and shall say unto them, The God of your fathers hath sent me unto you; and they shall say to me, What is his name? what shall I say unto them? 14 And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you. (Exodus 3:13-14)
So when Jesus, in John 8:58, stated “Before Abraham was, I am”, the Jews knew exactly what He was saying. Jesus was stating, in no uncertain terms, that He is the same God who spoke to Moses–the great I AM. This infuriated the Jews because they understood that as blasphemy and deserving of death. This was further reinforced by Jesus’ conveying that He existed before Abraham.
Jesus was very clear. He is God because He is the I AM.