The conversation begins way back at verse 13 where the Pharisees accuse Jesus of testifying about himself, which thing is inadmissible under the law:
So the Pharisees said to him, “You are bearing witness about yourself; your testimony is not true.” Jesus answered, “Even if I do bear witness about myself, my testimony is true, for I know where I came from and where I am going, but you do not know where I come from or where I am going.
You judge according to the flesh; I judge no one. Yet even if I do judge, my judgment is true, for it is not I alone who judge, but I and the Father who sent me. - John 8:15-16
This theme carries throughout the passage...Jesus refusing to respond in the way that the people he is among expect him to respond. They perceive him as merely a man and Jesus keeps insisting that they misunderstand that he and the Father are one.
In your Law it is written that the testimony of two people is true. I am the one who bears witness about myself, and the Father who sent me bears witness about me.” They said to him therefore, “Where is your Father?” Jesus answered, “You know neither me nor my Father. If you knew me, you would know my Father also.” - John 8:17-19
He said to them, “You are from below; I am from above. You are of this world; I am not of this world. I told you that you would die in your sins, for unless you believe that I am he you will die in your sins.” - John 8:23-24
They said to him, “We were not born of sexual immorality. We have one Father—even God.” Jesus said to them, “If God were your Father, you would love me, for I came from God and I am here. I came not of my own accord, but he sent me. Why do you not understand what I say? It is because you cannot bear to hear my word. - John 8:41b-43
By the time we get to verse 50 the Jews are accusing him of being a Samaritan (excluded from full inclusion in God's people) and being possessed:
The Jews answered him, “Are we not right in saying that you are a Samaritan and have a demon?” Jesus answered, “I do not have a demon, but I honor my Father, and you dishonor me. Yet I do not seek my own glory; there is One who seeks it, and he is the judge. - John 8:48-50
Again responding in an unexpected way, Jesus acknowledges that they are dishonoring him but he doesn't care. He is not seeking "his own glory" in the sense that he does not need to be esteemed in the eyes of other men. The only glory (substantiation) he accepts is that which comes from the Father. This is why Jesus consistently entreats people to believe him because of the words he speaks and, if they will not hear his words, at least believe because of the works that he does. His words are the Father's words and his works are the Father's works because he is in the Father and the Father is in him.
If you had known me, you would have known my Father also. From now on you do know him and have seen him.” Philip said to him, “Lord, show us the Father, and it is enough for us.” Jesus said to him, “Have I been with you so long, and you still do not know me, Philip? Whoever has seen me has seen the Father. How can you say, ‘Show us the Father’? Do you not believe that I am in the Father and the Father is in me? The words that I say to you I do not speak on my own authority, but the Father who dwells in me does his works. Believe me that I am in the Father and the Father is in me, or else believe on account of the works themselves. - John 14:7-11
Phillip: Show us the Father
Jesus: You still don't know me? I am in the Father and the Father is in me.
There is a similar thought in John 7:15-18:
The Jews therefore marveled, saying, “How is it that this man has learning, when he has never studied?” So Jesus answered them, “My teaching is not mine, but his who sent me. If anyone's will is to do God's will, he will know whether the teaching is from God or whether I am speaking on my own authority. The one who speaks on his own authority seeks his own glory; but the one who seeks the glory of him who sent him is true, and in him there is no falsehood.
So now we come to the verse in question:
Are you greater than our father Abraham, who died? And the prophets died! Who do you make yourself out to be?” Jesus answered, “If I glorify myself, my glory is nothing. It is my Father who glorifies me, of whom you say, ‘He is our God.’ But you have not known him. I know him. If I were to say that I do not know him, I would be a liar like you, but I do know him and I keep his word. Your father Abraham rejoiced that he would see my day. He saw it and was glad.” So the Jews said to him, “You are not yet fifty years old, and have you seen Abraham?” Jesus said to them, “Truly, truly, I say to you, before Abraham was, I am.” So they picked up stones to throw at him, but Jesus hid himself and went out of the temple. - John 8:53-59
Q: Are you greater than Abraham?
A: I'm not out to glorify myself, my glory comes from God and you don't know him or me. Abraham knew me.
Q: You've seen Abraham, huh?
A: I am before Abraham
What they wanted from Jesus was a yes or no answer. They wanted Jesus to either defend (glorify) or disavow himself in the face of critical human scrutiny as any man would. That is not who he is or why he came. One may put God in the dock but He is not subject to human judgement.
And as he was in Jerusalem, in the passover, in the feast, many believed in his name, beholding his signs that he was doing; and Jesus himself was not trusting himself to them, because of his knowing all men , and because he had no need that any should testify concerning man, for he himself was knowing what was in man. - John 2:23-25