Why does Macbeth want to kill Macduff in Shakespeare's "Macbeth"?
Fear. In his soliloquy of Act III of "Macbeth," Macbeth admits this to himself:
To be thus [king] is nothing, but [unless] to be safely thus--/Our fears in Banquo stick deep,/And in his royalty of nature reigns that/Which would be feared....(III,i,48-51)
Since hearing the predictions of the weird sisters, Macbeth has been motivated by amition and fear. After all, it is Lady Macbeth who promises to give him the courage to enact his first murder:
This night's great business into my dispatch;/Which shall to all our nights and days to come/Give solely sovereign sway and masterdom. (I,v,67-69)
Although Macbeth has been described as brave on the battlefied, his "bravery" is ferocious, he overkills in his fear that anyone retaliate against him. After hearing that he will not be killed by a man "born of a woman," Macbeth, ridden with both fear and guilt, becomes a bit paranoic. As Frost wrote in his poem "The Road Not Taken," "Yet knowing how way leads to way," Macbeth's murderous path to ambition has no end but his own.
Macbeth has been told my the witches that he will not be killed by a man born of a woman, but to beware of Macduff. While Macbeth chooses to use the witches predictions as an indication that he will reign as king for a long time, he is still disturbed by the warning against Macduff and wants to ensure that he is completely safe. Therefore, he decides to kill Macduff and Macduff's family. Ironically, Macbeth's failed attempt to kill Macduff but successful murder of Macduff's family is what finally spurns Macduff to kill Macbeth himself.