Why is macbeth involved in an external conflict with banquo

When the witches told Macbeth his prophecy (that he would be Thane of Cawdor and then King) Banquo was with him. Banquo asked what his prophecy was, and the witches told him his children would be kings. So even though Macbeth will be king, Banquo's children with eventually have the throne. Once Macbeth becomes King, he gets greedy andn believes Banquo "stole" that from him. He wants his own children to be kings. So he decides to have Banquo and Fleance (Banquo's son) killed so there is no chance of Banquo's children taking the throne. He hires murderers to kill both of them, but they only succeed in killing Banquo. Fleance escapes.