Not because he is mean; he is not at heart a cruel man. But he has been so tortured by jealousy that he is angry with Desdemona all the while he still desperately loves her. The outrage is not only that he hits her (that's bad enough) but he hits her in public. Nobody who knew them in Venice can believe it.
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This happens in Act IV Scene 1. Ludovico has been sent from Venice with orders that Othello is to return to Venice leaving Cassio in charge in Cyprus. Othello by this point is "horn-mad", obsessed with the belief, implanted so cleverly by Iago, that Desdemona is having an affair with Cassio. So when Othello hears Desdemona explain to Ludocivo that Othello and Cassio are estranged, and that she hopes that they will reconcile "for the love I bear Cassio", Othello hears this as an admission by Desdemona that she is having a love-affair with him. And an admission made brazenly in public! He starts to get uncontrollably angry. Then Desdemona says she is glad to hear about Cassio's promotion. Another admission! thinks Othello. He loses it completely and hits her. Desdemona protests that she has done nothing wrong, and Ludovico is aghast at this patently wrong behaviour and implores Othello to apologise, which he refuses to do.
He is one of the commanders but raised in position by othello as liutenant.
Desdemona slept with Othello in the play. And despite what Othello thought, he was the only guy she slept with.
Because Othello is unsure of Desdemona's actions. He is afraid of losing Desdemona to Cassio.
Desdemona's handkerchief, given to her as a wedding present from Othello, is a symbol of something precious between Desdemona and Othello.
Desdemona goes to Lago for advice about what to do about Othello's accusations. This is when Othello asks Emilia to go and find Desdemona while accusing her of harlotry.