Why is it said that Banquo's son would become king although it was Malcolm, Duncan's son, who took over after the death of Macbeth?
It is actually foretold that Banquo's descendents would become kings in the future - "Thou shalt get kings, though thou be none" (1.3). Also, consider the prophecy shown to Macbeth in Act IV, scene 1:
Thy crown does sear mine eyeballs. And thy hair,
Thou other gold-bound brow, is like the first.
A third is like the former. Filthy hags!
Why do you show me this? A fourth! Start, eyes!
What, will the line stretch out to the crack of doom?(130)
Another yet! A seventh! I'll see no more:
And yet the eighth appears, who bears a glass
Which shows me many more; and some I see
That twofold balls and treble sceptres carry:
Horrible sight! Now I see ’tis true;(135)
For the blood-bolter'd Banquo smiles upon me,
And points at them for his. What, is this so?
Fleance, Banquo's son, escaped the murder attempt that killed his father, thus allowing him to live and produce generations descended from Banquo. It was believed during Shakespeare's times that King James I of England was a descendent of Banquo, so one must consider the fact that Shakespeare was writing for the times and for the person in power at the time.
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It is important to remember that Macbeth was probably written during the early reign of James I, who was supposedly related to the real Banquo. James 1, who was first King of Scotland, succeeded his cousin Queen Elizabeth because she was childless and James was her closest Protestant relative. The witches do not say exactly when Banquo's sons will be kings. At the time of Banquo's murder, Fleance is rather young and so it would be natural for the older Malcolm, who had been named successor to Duncan, to take over as king, Audiences at the time would have associated the witches' prophecy with James I, not necessarily Fleance. And thus Banquo's offspring did inherit an even larger throne than Malcolm or Macbeth.
because the king in shakespeare time was king James I. and James was a descendant of Banquo, so by adding this prophecy Shakespeare knew James would like the play, this is also why he added witches and why is was set in scotland. to have a king approve of yor work was a big thing back then.