Why did Macbeth kill Duncan?
Macbeth kills Duncan because the witches first give him the idea, his wife gives him the plan, and both (idea and plan) reinforce his blind ambition to be king.
Macbeth has doubts about killing Duncan: he is his kinsman (relative); he has honored Macbeth of late (given him the title Thane of Cawdor for valor in battle); plus, Macbeth is his host and subject. Murder obviously violates the Thane-King bond ("comitatus"). Not to mention that Duncan is meek and virtuous.
But, against all this Macbeth says (Act I, scene vii):
I have no spur / To prick the sides of my intent, but only / Vaulting ambition, which o'er-leaps itself, / And falls on the other.
Also, Lady Macbeth challenges Macbeth's manhood and stirs up his bloody courage ("screw your courage to the sticking place"). She calls him a coward if he doesn't go through with her plan. She says he is "too full the milk of human kindness" and admits that she would "dash out the brains" of her own child "had I sworn as you / Have done to this." Such is her resolve.
After this, Macbeth agrees to kill Duncan, saying:
I am settled, and bend up Each corporal agent to this terrible feat. / Away, and mock the time with fairest show: / False face must hide the false heart doth know.
In other words, Macbeth knows he must go against Time and put on an act to cover up his heinous intentions.