Most likely, it is the case. His wealth, social status and even marriage were due to his military successes.
In every other matter, he was an outsider, and he was constantly reminded of that. Brabantio told that
> To fall in love with what she feared to look on?
> It is a judgment maimed and most imperfect
> That will confess perfection so could err.
Even his wife, when summoned by the Duke, firstly referred to him as "Moor" and only then as "Othello".
> And so much duty as my mother showed
> To you, preferring you before her father,
> So much I challenge that I may profess
> Due to the Moor my lord.
Most probably, when constantly reminded that he is different, unworthy of love etc. anyone will start feeling inadequate no matter how strong-willed they are.
_(Only adding my own answer as there are no alternative answers. This is the initial version, I will add more details later.)_