Macbeth’s ambition leads to his death because once he has what he wants, he is afraid to lose it and makes rash decisions.
Macbeth wanted to be king once the witches prophesized his kingship. His wife developed a plan to kill the current king and he carried it out. Yet once king, he did not feel secure.
To be thus is nothing,
But to be safely thus. (Act 3, Scene 1, p. 42)
Macbeth’s first act as king was to plan his friend and noble Banquo’s death. Macbeth knew that Banquo heard the same prophecies he had, and therefore might suspect him. He also feared Banquo because the witches prophesized that his sons would be king.
Killing Banquo was not enough. Macbeth then finds himself putting spies throughout his kingdom, and worrying about Macduff and others. He has Macduff’s entire household killed, leading the fiery Macduff to vow revenge. Macduff worked closely with Malcolm, the rightful heir, and it was he who killed Macbeth in the final battle.
Hail, King! for so thou art. Behold where stands
The usurper's cursed head. The time is free. (Act 5, Scene 3, p. 90)
In the end, it is Macbeth’s constant ambition and paranoia that leads to his downfall and death because, once begun, he goes too far and kills too many friends and makes too many other rash decisions.