Macbeth wants Banquo and Fleance killed primarily because of the witches' prophecy. The witches predicted that Macbeth would become king, but they also foretold that Banquo’s descendants—not Macbeth’s—would inherit the throne.
Even though Macbeth has already secured the crown by murdering King Duncan, he realizes that his rule is insecure as long as Banquo and his son, Fleance, are alive. Macbeth acknowledges that Banquo is the only man in Scotland whom he fears because Banquo possesses a wise and noble character.
Additionally, Fleance, as Banquo’s son, represents a direct threat to Macbeth’s legacy. If the prophecy is true, Macbeth’s reign will be meaningless since his bloodline will not continue on the throne.
To prevent Banquo’s heirs from taking the crown and to secure his power, Macbeth hires two murderers to kill Banquo and Fleance.
This act shows how Macbeth, once hesitant about killing Duncan, has now fully embraced violence and paranoia to maintain his rule.