What does John 8:41 mean?

Jesus has been using the idea of fatherhood to explain why the religious leaders opposing Him are not "true sons" of Abraham. Children inherit their nature from their fathers. So, those who are the actual spiritual children of Abraham will do what Abraham did, which was to obey God and respond to His message. The men attempting to kill Jesus (John 5:18) are rejecting the message of God, because they are rejecting the messenger of God (John 6:29). They are enslaved to sin (John 8:34) because they refuse to accept the only One who can set them free (John 8:31–32). As further proof, Jesus points out that their actions reflect their father—and neither God nor Abraham are associated with lies and murder.

Here, the conversation takes a nasty turn. Prior to this, the crowd's attacks on Jesus have been somewhat formal. They have disputed His claims, condemned His words, and even tried to have Him arrested or killed (John 5:18; John 7:32). In this moment, though, they resort to outright personal insults. The statement "we were not born of sexual immorality" is a direct slur against Jesus, whose birth was a subject of some controversy (Luke 1:30–38). In short, the critics are smearing Jesus' reputation by calling Him an illegitimate child.

Jesus' response shows that He is not the passive, soft, weak-eyed cartoon character so often imagined. Instead, He forcefully repeats His claim that these men reject Him because they reject God—they are the spiritual children of Satan (John 8:44)! This turmoil will escalate until Jesus once again claims to be God incarnate, at which point the crowd will resort to violence (John 8:59).