Banquo shows that he will become an antagonist in scene 3 of Macbeth when he....?

When the Weird Sisters tell Banquo that he will father kings, it begins to set him up as Macbeth's antagonist because they tell Macbeth that Macbeth will be king.  It doesn't take very long, after Macbeth commits the murder of Duncan, for him to realize that, if Banquo's descendants are going to be kings, then this means that he will not pass the crown on to his own family.  Macbeth cannot know in what way...

When the Weird Sisters tell Banquo that he will father kings, it begins to set him up as Macbeth's antagonist because they tell Macbeth that Macbeth will be king.  It doesn't take very long, after Macbeth commits the murder of Duncan, for him to realize that, if Banquo's descendants are going to be kings, then this means that he will not pass the crown on to his own family.  Macbeth cannot know in what way Banquo's family will assume the throne -- will Macbeth fail to have children? will Banquo and his family overthrow Macbeth and take power? -- and so Banquo's prophecy thus becomes the force that eventually prompts Macbeth to take action against him.

Further, Banquo's suspicion of the Weird Sisters' words and intentions sharply contrasts Macbeth's total acceptance and trust of them.  Banquo says,

But ’tis strange.
And oftentimes, to win us to our harm,
The instruments of darkness tell us truths,
Win us with honest trifles, to betray ’s
In deepest consequence.  (1.3.124-129)

He is immediately concerned that the Sisters have told Macbeth one small truth in order to win his trust, then they told him something even larger -- knowing he will believe it -- to see what he will do to make that second thing happen.  Macbeth believes that the Weird Sisters know his fate, but Banquo is concerned that they might be manipulating Macbeth in order to see what terrible things he might do to make that future happen; Banquo seems to believe in free will rather than fate.  Banquo's suspicion of the prophecies as well as his immediate concern that it is possible for Macbeth to be manipulated in this way make him a threat to Macbeth as well.