To answer this question, you would first need to determine your own interpretation of what the true source of Othello's tragedy is. If it does stem from a personal weakness, for example, what specifically is Othello's weakness? On the other hand, you might also claim that his tragedy does not actually stem from some inborn personal weakness at all, but rather emerges from some alternative influence altogether, one which should be held as separate from the larger social context that surrounds him.
In any case, I think one way of arguing against this statement is to focus on Othello's relationships and his personal decision-making. Ultimately, I think there's a strong argument that Othello's great error can be viewed as a matter of faith. Time and time again, what we see in the play is Othello placing his trust in the one person he ought not to place such faith in (Iago), even as he refuses to extend that same faith to his own wife (who remains faithful to Othello himself). This leads him on a road towards jealousy and abuse against Desdemona, culminating in his murdering her at the end of the play.
Ultimately, then, I would argue that Othello's tragedy lies first and foremost on the level of the deeply personal. With that in mind, I think collapsing Othello into a tragedy about larger social contexts, as your question seems to do, might actually risk obscuring those deeply personal failings and betrayals, and the very real responsibility and culpability Othello has over his own actions and decisions.