Othello is certainly a tragic hero given that he fits the definition perfectly. His downfall is brought about by an error in judgment, not by depravity or some kind of evil motive. So if you were going to try and prove that he was not a tragic hero, you would have to explain that his murder of Desdemona was driven by depravity, by some kind of weakness within Othello. You might also focus on the fact that he was so easily manipulated by Iago but you would also have to be careful to avoid the error of judgment side of the equation. Since Othello trusted Iago so completely, the judgment error is rather obvious and again would take some serious work to explain it away.
Since you want to show that he is responsible, you might focus on the early stages of his wooing Desdemona, when he chose to ignore the warnings of others and even his own feelings of caution since he knew that Desdemona ran in a very different circle than he did and he knew that Brabantio would not be exactly pleased with her choice.