In Act IV, Scene II of Macbeth, Lady Macduff is informed by Ross that Macfuff has gone to England. She says that to flee in this way makes him look like a coward and a traitor. "When our actions do not, / Our fears do make us traitors" (IV.ii.3-4). Ross tells her that Macduff knows what he is doing and he tells her that they are all under suspicion, "But cruel are the times when we are traitors / And do not know ourselves;" (IV.ii.18-19).
Lady Macduff then tells her son that his father is dead. He disagrees. She tells him he is a traitor, explaining what a traitor is. Lady Macduff insists that traitors should be hanged. Even if Macduff is still alive, she believes he will be killed. She has lost complete faith in him. The dialogue between Lady Macduff and her son can seem distraught but also cold. Her son notes to her:
"If he were dead you'd weep for him. If you would not, it were a good sign that I should quickly have a new father." (IV.ii.61-63)
A messenger warns Lady Macduff to flee but she has done nothing wrong so she sees no point in fleeing. However, she doesn't heed Ross' advice that she too is under suspicion. The murderers arrive and kill them both. The son denies that his father is a traitor as he is killed.
Lady Macduff feels abandoned. She is too stubborn or honorable to accept that she should also leave. Her son doesn't believe his father is dead and he even questions her loyalty, saying if she is not weeping, it is a good sign that he will have a new father. Therefore, the son remains loyal to his father to the end.
In the overall plot of the play, this is an example of how Macbeth is able to cast suspicion from himself onto others. Here, by driving Macduff out of Scotland, he makes him (Macduff) look suspicious. Lady Macduff thinks that even if Macduff is not a traitor, his actions make him a coward. By refusing to leave, Lady Macduff shows strength of conviction but she also shows a certain stubbornness.