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.