In Othello, why does Iago tell Othello that Brabantio badmouthed him?

You are refering to Act I scene 2 which introduces Othello
and Iago talking about Othello's marriage to Desdemona and how Brabantio is opposed to
it. Let us remember what has happened before this scene. Iago has persuaded Roderigo to
deliberately stir up Brabantio, alterting him to the way that Desdemona has secretly
married Othello without her father's permission. If you look carefully at what Iago says
to Brabantio, and the kind of animal sexual imagery he uses, he is deliberately stirring
up Brabantio to cause problems for Othello. In the same way, therefore, in this scene,
we see Iago trying to stir up Othello against Brabantio to make the inevitable conflict
between them that more heated. Note what he tells Othello about
Brabantio:

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Nay, but he
prated

And spoke such scurvy and provoking
terms

Against your
honour,

That with the little godliness I
have

I did full hard forbear
him.

Iago thus tries,
unsuccessfully, to stir up Othello's anger against Brabantio in teh same way that he has
already successfully achieved this goal with Brabantio in Act I scene
1.