Why is this play a tragedy? in act 5

Othello kills his wife, the love of his life, before learning the truth. Othello's murders of both Desdemona and Iago are dishonorable. He kills Desdemona in a jealous rage, and he murders Iago in anger. Unfortunately, he takes no responsibility for either act, believing himself to have been wronged. He never admits that his own flaws were partially responsible for his behavior, and that is where the true tragedy is found.