52 Then the Jews said to Him, “Now we know that You have a demon! Abraham is dead, and the prophets; and You say, ‘If anyone keeps My word he shall never taste death.’
53 Are You greater than our father Abraham, who is dead? And the prophets are dead. Who do You make Yourself out to be?”
54 Jesus answered, “If I honor Myself, My honor is nothing. It is My Father who honors Me, of whom you say that He is your God.
55 Yet you have not known Him, but I know Him. And if I say, ‘I do not know Him,’ I shall be a liar like you; but I do know Him and keep His word.
death (back in verse 51) refers to eternal death (in the Greek), but the Jews were referring to physical death. And they forgot about Elijah, conveniently.
They could imagine nobody greater than Abraham (v. 53) except God.
Jesus' identity was centered on His relationship with the Father (v. 54). Without that, His glory would be nothing.
To "honor" is to do or speak that of a person which shall not only manifest our own esteem for him, but shall lead others to esteem him too. The Father's esteem for the Son is evidenced by His love and admiration for Him, as well as His desire to make Him the loved and admired of others. God honored Him at His birth, by sending angels to herald Him as Christ the Lord. He honored Him during the days of His infancy, by directing the wise men from the east to come and worship the young King. He honored Him at His baptism, by proclaiming Him His beloved Son. He honored Him in death, by not surrering His body to see corruption. He honored Him at His ascension, when He exalted Him to His own right hand. He will honor Him in the final judgment, when every knee shall be made to bow before Him and every tongue confess that He is Lord. And throughout eternity He shall be honored by a redeemed people who shall esteem Him the Fairest among ten thousand to their souls. Infinitely worthy is the Lamb to receive honor and glory. — Exposition of the Gospel of John, Volume 2, by Arthur W. Pink, page 54.