What does John 8:45 mean?

Jesus is hammering His critics for their hypocrisy. While they profess to be sons of Abraham, their actions contradict that claim. Children follow the nature of their fathers, doing what their fathers do (John 8:39). So, those who are "true sons" of Abraham should be obeying God (John 8:40). Instead, these men are being dishonest (John 8:13–15), violent (John 5:18; John 8:59), and obstinate (John 8:43). This suggests that their spiritual father is, in fact, one marked by lies and murder and rebellion: the devil (John 8:44).

In prior verses, Jesus has pointed out that a person's willingness to accept God always comes before their ability to understand. Those who will not obey cannot understand. In other words, they do not reject God because they don't grasp His message—they fail to grasp the message because they don't want to accept it. Here, Jesus more or less says the same thing, for a third time in this gospel (John 7:17; John 8:43). The reason these men reject His words is because they prefer lies, and since what Jesus says is true, they are committed to ignore it.