What does John 8:38 mean?
A major point of pride in the nation of Israel was their descent from Abraham. As the man given a promise by God, Abraham represents an anchor point for the Jewish understanding that they are God's chosen people. In trying to dispute Jesus' claims to spiritual truth, the religious leaders of Jerusalem have misinterpreted His references to His "father." Their claim, in response, was to profess their descent from Abraham. As Jesus has pointed out, however, being a part of God's family is driven by faith and spirit, not by genealogy. The "true" children of Abraham are those who obey God, which includes following His Son, Jesus Christ (John 6:29). As Abraham followed God, so too will his spiritual children.After claiming that the people opposing Him are not really sons of Abraham, Jesus now begins to refer to "your father," meaning the spiritual father of these obstinate critics. While Jesus comes by the will of God and does what His Father wants Him to do, the people who seek to kill Him (John 5:18) are acting in the example of their father. Jesus will subtly make this point several times before outright naming the true spiritual father of His enemies: the Devil (John 8:44)!
Unsurprisingly, this escalation leads Jesus' critics to resort to insults (John 8:41), accusations of insanity (John 8:48), and another attempt on His life (John 8:59).