Betrayal is a huge part of Macbeth. The play opens with a battle that is being fought because two of the Thanes (Lords) who are supposed to be serving King Duncan have turned against him. In the first act of the play, he has put down the rebellion.
So, in this opening of the play and throughout the rest of the play, betrayal is motivated by a desire for power, to gain status, and for Macbeth, the central figure who betrays many, the desire to become and remain King.
Macbeth betrays King Duncan (to whom he has sworn allegiance) by killing him when he is a guest at his home. Why? To gain the crown that Duncan wears. He also betrays his friend Banquo. Why? To retain the power and position of being King. The witches had prophesied that Banquo's children would be kings, and Macbeth wants to prevent this by killing Banquo and his son Fleance. He misses Fleance, but gets Banquo.
And you could also make a case that Macbeth betrays Macduff when he murders his family. Why? He is afraid that Macduff will be the agent of his fall from power.
So, Macbeth is the main betrayer in the play, and his motivation is the gaining and maintaining of power.
Macbeth betrays King Duncan by killing him because he wants to be king and he thinks thats the only way it will happen. Lady Macbeth also helped in the killing of King Duncan as well.