What does John 8:39 mean?
Jesus has just explained that being part of God's family is a spiritual matter, not a question of genealogy. The Jewish religious leaders who seek to kill Him (John 5:18) are descended from Abraham. But they are not true "sons" of Abraham because they do not accept the One sent by God (John 6:29). To support this, Jesus used the analogy of a household servant who lives in the home and knows "about" the master but who has no real rights to the house. A true son, on the other hand, has a permanent relationship (John 8:35). Spiritually, this is the case with those who are in Abraham's family tree but do not follow God. Since they do not do what Abraham did—obey God—they cannot be "true sons" of God the Father.The critics, seemingly confused about the meaning of this, once again state that they are children of Abraham. This repeated reference might also be a subtle insult to Jesus, by hinting at His scandalous birth. Later, this subtlety will be gone and the crowd will outright accuse Jesus of being an illegitimate child (John 8:41).
Here, Jesus takes a slightly different approach. In the prior verse, He spoke to the hostile crowd about "your father," meaning someone other than Abraham or God. Here, He begins to point out that the actions of these critics prove their real spiritual state. They don't do as Abraham did, so they are not Abraham's children. Instead, their actions imitate the Devil, their true (spiritual) father (John 8:44).