Othello didn't realize that Desdemona was falling for him when he started talking with her, so Desdemona actually had to make the first move. Othello reports that she told him, "if I had a friend that loved her, /I should but teach him how to tell my story. / And that would woo her." So, Othello might have been missing more subtle clues, making him a rather shy man in matters of love when most men of the day were more aggressive. However, even the Duke acknowledges that a woman would find this attractive, saying his own daughter would fall for that. Othello's honesty with Desdemona about his slavery and the wars, topics that other men of the day would have avoided as inappropriate, shows that his love is not based having a true friendship with her.
Beyond the unusual friendship hinted at, Othello also has incredible trust in Desdemona, putting his own life in her hands when he tells the Duke to "let her speak of me before her father" and that if she speaks badly of him, the Duke should take his life. Othello would have Desdemona to stay home during the war, but when she insists she wants to come, Othello yields to her request. This willingness to share power is reinforced when he calls her "fair warrior" after they're reunited in Cyprus. So, before Iago's manipulations, Othello is open, honest, and willing to share authority with the one he loves.