In Macbeth, what is the source of Macbeth's anger toward Macduff?
Macbeth is not really angry at Macduff but he comes to fear him greatly, owing to the prophecies of the Three Weird Sisters. They warn him to beware of Macduff. Macbeth therefore takes measures against him such as slaughtering his family while he is in England. In this way Macbeth incurs Macduff's lasting emnity.
Macduff acts as a foil, or contrast, to Macbeth. While Macbeth is murderous and corrupt, Macduff provides some moral grounding to the play. Although he is not without his faults, he is presented in the main as an honourable and conscientious man. This is shown in his reaction to his family's deaths. He is genuinely grieved for them, and not afraid to show it (whereas the Macbeths consider any show of emotion a weakness), and he also proves his mettle by instantly deciding to act against the murderer.
Macduff appears as Macbeth's opposite not just in terms of character but also in terms of the play's action. After Macbeth kills Duncan, Macduff is the first one to raise the alarm:
Confusion now hath made his masterpiece;
Most sacrilegious murder hath broke ope
The Lord's anointed temple and stolen thence
The life o' the building. (II.iii.63-66)
Macduff is instantly aware of what the murder means for the land, the horror and 'confusion' that will be engendered by this wicked deed. Also, of course, Macduff is the one who finally despatches Macbeth, thus purging the land of its evil. He is instrumental in restoring the order that Macbeth destroyed.
Initially, the Three Weird Sisters warn Macbeth about Macduff, which causes Macbeth to view him with suspicion. Macbeth also knows that Macduff supports Malcolm, who is in England attempting to rally troops to battle against Macbeth's forces. Since Macbeth's ultimate goal is to preserve his title as king, he views Macduff as a threat and knows that he will challenge his authority. One could assume that Macbeth is angry with Macduff because he openly supports Malcolm. Malcolm is King Duncan's son. He is the rightful heir to the throne, and he fled Scotland immediately after his father's assassination. Macbeth knows that Macduff is helping Malcolm, who wishes to usurp power and become king. Following the second set of prophecies, the possibility of Macduff ending Macbeth's reign begins to haunt him, and Macbeth hires assassins to murder Macduff's family. Overall, Macbeth is angry at Macduff for siding with Malcolm and attempting to challenge his authority. Macbeth's decision to murder Macduff's family only motivates Macduff to kill Macbeth and end his reign.