Desdemona and Cassio are firm friends, and Iago intends to use this to his advantage. He knows that Desdemona, whilst in love with Othello, loves Cassio as her "best" friend. He is something of an intellectual, rather than a respected, valiant soldier which contributes to Iago's complete contempt for him. Why would Othello promote a man "That never set a squadron in the field" (I.i.22)?
Cassio is all reputation and title with no real substance
according to Iago and, when he has a brawl which Iago himself orchestrated and is demoted by Othello and disgraced, Iago encourages him to ask Desdemona to plead his case with Othello.
Desdemona does not question Cassio's intentions but things are never "as they seem" in Othello, and she is more than happy to speak to Othello. She walks into Iago's trap as he has already sewed the seed in Othello's mind that she may be involved with Cassio.
It is clear then that Desdemona has no idea that by speaking to Othello she will raise questions about her own fidelity. When she asks Othello to "call him back" (III.iii.50) so that Cassio can plead his case, and then becomes somewhat persisitent when Othello is not keen to do so, she is contributing to her own demise. Othello will "deny thee nothing" but as soon as she leaves, Iago is there continuing his quest to persuade Othello.
Othello's jealousy and fear that Desdemona could love him a man so different from her in,''clime, complexion, and degree'' (III.iii.230) aids Iago's plan and he is able to use coincidence several times in order to fill Othello's thoughts with “this pestilence.”