Commentaries:
Spiritually, Satan has been our father. We already have had his mark placed on us, and in our lifetime we have shown his characteristics. That is exactly what Jesus is talking about here: He knew that Satan was the spiritual father of these people because they carried his mark in the way they reacted to Him and each other.
Abraham had God as his spiritual Father, and Abraham did not attempt to kill the One who became Christ—in fact, He was hospitable to Him and honored Him. He was not hostile to Him in any way, but instead did everything in his power to submit to Him. But here were the people of Jesus' time trying to put Him to death. They were openly hostile to Him.
Our problem is not worrying about taking on Satan's mark—we already have it. Our concern is to control and overcome it because God is now our Father, and He has already enabled us to resist that mark in our lives. It is our worshipful duty to work with God, to strive to break free of that foul spirit's enslaving hold on us.
John W. Ritenbaugh
The Spiritual Mark of the Beast
He uses the words "father" and "children" in a well-accepted, spiritual way—that is, a son or a daughter can be considered the child of another if he or she shows the nature and works of that other person. Thus a "son of Belial" shows the characteristics of Belial, meaning confusion, though he is not physically Belial's child. A "son of Abraham," then, would behave or live as Abraham did.
John W. Ritenbaugh
The Holy Spirit and the Trinity (Part Three)
Other Forerunner Commentary entries containing John 8:39:
Genesis 3:15
Malachi 3:1
Matthew 12:22-50
Matthew 13:33
Romans 8:14-17
Romans 9:7
Galatians 3:2
Galatians 3:7
Galatians 4:5