Self-deprecation may be a gesture of meekness, like a dog that shows its belly: a sign that you mean no harm, or are not worth harming. It may be calculated to lower expectations: whether out of discretion, not to disappoint them, or by design, to surprise them. Or it may be an indulgence, extorting praise by threatening self-harm.
(In this way self-deprecation helps define friendship: what is a friend but someone who praises you for what you regret, someone who finds unthinkable the things you fear may be true? These precious offices can only be performed when self-deprecation occasions them.)
It may be a way to evade responsibility. “I couldn’t X to save my life” is a polite way to say no when it was wrong to ask. And it avoids embarrassment: perhaps you could X, if you put your mind to it, but when there is nothing to gain, why risk failure when you can excuse abstention?
Of course self-deprecation is not always serious. It may be an indirect boast. “All censure of a man’s self is oblique praise. It is in order to show how much he can spare.” Which is harmless in moderation. Or it may be a provocation. Montaigne appalled his friends by insisting that he had no memory. In the French of the time memory stood for intelligence: but Montaigne made the distinction, and his self-deprecation enforced it.
All these uses are legitimate, but none of them can excuse the habit of self-deprecation. If you expect others to take you seriously, you should try it for yourself. Tell me often enough how stupid and useless you are and I may begin to believe you; apologize for yourself often enough and I will begin to believe you have something to be sorry for.
Of course some lives are just that lost, some people are just that broken; if patience can help them, they have a right to it. But I have no patience for people who fear being resented more than they fear being despised. It doesn't even work.
You may resent people for having things you can never have; but the people you hate are the ones who have the things you can never have, but despise them.
Aristocracy was invulnerable as long as aristocrats took pains to enjoy, and be seen to enjoy, their wealth and privilege; but the moment they started to doubt themselves the masses rose up and devoured them and raised the clear conscience of plutocracy in their place.
All persuasion begins in confidence. And since respect will be given, if those who deserve it cannot stand by their words, deeds, and lives, others will receive it undeservingly.