From the moment that Macduff sees King Duncan's bloody body lying dead in Macbeth's castle in act 2, scene 3 of William Shakespeare's Macbeth, Macduff suspects that Macbeth and Lady Macbeth were involved in Duncan's murder. Macbeth soon senses that Macduff suspects him of the murder, and an uneasy relationship between the two men begins.
When Macduff fails to attend Macbeth's coronation (2.4.47), and Macduff also declines to attend Macbeth's coronation banquet (3.4.156–157)—even though all of the Lords and Thanes of Scotland were in attendance, including the ghost of Banquo—Macbeth is certain that Macduff has become his enemy.
The appearance of Banquo's ghost at Macbeth's coronation feast unnerves Macbeth, and Macbeth decides to visit the witches who first prophesied that he "shalt be King hereafter!" (1.3.53) and demand that they tell him what the future holds for him now that he's become king.
Macbeth goes to the witches, who produce four apparitions for Macbeth, and the first thing that the first apparition says to Macbeth is "Beware Macduff" (4.1.78–79). Macbeth already knew this, and demands to know more. The second apparitions tells Macbeth that "none of woman born / Shall harm Macbeth" (4.1.89–90).
Macbeth interprets this to mean that Macduff, being born of a woman just like everyone else, can't harm him. However, Macbeth fails to realize that what the second apparition tells him doesn't necessarily negate what the first apparition tells him.
Nevertheless, to ease his fears about Macduff, Macbeth decides to have him killed.
MACBETH. Then live, Macduff. What need I fear of thee?
But yet I'll make assurance double sure,
And take a bond of fate: thou shalt not live (4.1.92–94).
After the witches disappear from the scene, Lennox arrives to tell Macbeth that "Macduff is fled to England" (4.1.158). This means that not only has Macduff gone to the country of England to join with Duncan's son, Malcolm, but also that Macduff has gone to the English king to ask for help in fighting against Macbeth.
Macbeth is upset with himself for not acting against Macduff sooner, so he resolves that in the future he won't hesitate to act as soon as the need arises.
MACBETH. From this moment
The very firstlings of my heart shall be
The firstlings of my hand (4.1.163–165).
Macbeth also decides to attack Macduff's castle and kill Macduff's family and anyone else in Macduff's ancestral line.
MACBETH. The castle of Macduff I will surprise,
Seize upon Fife; give to the edge o’ the sword
His wife, his babes, and all unfortunate souls
That trace him in his line (4.1.167–170).
Macbeth's intent seems to be to destroy Macduff and weaken his resolve against Macbeth by murdering Macduff's family and seizing all of Macduff's lands and property. If Macbeth's intent was to frighten Macduff and cause Macduff to resign himself to Macbeth's rule, Macbeth failed miserably.
Macduff returns from England with Malcolm, leading an army against Macbeth. Macbeth meets Macduff on the battlefield, and Macbeth unfortunately reminds Macduff of the death of this wife and children. This only heightens Macduff's need to avenge his family's murder.
It's Macbeth's resolve that's weakened when Macduff tells him that he was "from his mother's womb / Untimely ripp'd" (5.8.19–20), and Macduff, "being of no woman born," kills Macbeth.