What does John 8:37-40 mean?

37 I know that ye are Abraham’s seed; but ye seek to kill me, because my word hath no place in you. 38 I speak that which I have seen with my Father: and ye do that which ye have seen with your father. 39 They answered and said unto him, Abraham is our father. Jesus saith unto them, If ye were Abraham’s children, ye would do the works of Abraham. 40 But now ye seek to kill me, a man that hath told you the truth, which I have heard of God: this did not Abraham. (John 8:37-40 KJV)

William Burkitt’s Commentary

The Jews boasting again that they were Abraham’s seed, and bearing themselves much upon it: our Saviour tells them, He knew they were so, his natural children according to the flesh: but not his genuine children according to the Spirit: this he proves, because they did not tread in Abraham’s steps, and do his works; for if either the temper of their minds, or the actions of their lives were agreeable to Abraham, they would not seek as they did, to destroy and kill him, only for bringing the doctrine of salvation to them, which he had heard and learned of the father.

Thence learn, 1. How prone we are to glory in our outward privileges, and to rely upon them. Whereas these are arguments of God’s goodness towards us, but no evidence of our goodness towards him.

2. That it is very dangerous and unsafe to pride ourselves in, and depend upon, any external privileges and prerogatives whatsoever: as our being born within the pale of the visible church, our descending from pious parents and holy progenitors; for unless we be followers of their faith, admirers of their piety, and imitate their example, we are none of their children; but belong to another father, as our Saviour tells the Jews in the other verses.