Self-conceit, n.
Conceit of one's self; an overweening opinion of one's powers or endowments.
Syn. -- See Egotism.
Shades of meaning
Fernald has no entry of its own for self-conceit; he lists it under egotism, pride.
Where he writes about it:
Self-assertion is the claim by word, act, or manner of what one believes to be his due; self-conceit is an overestimate of one's own powers or deserts. — from egotism
Conceit is a briefer expression for self-conceit, with always an offensive implication; self-conceit is ridiculous or pitiable; conceit arouses resentment. — from egotism
Self-assertion at times becomes a duty; but self-conceit is always a weakness. — from egotism
Self-esteem is more solid and better founded than self-conceit; but is ordinarily a weakness, and never has the worthy sense of self-confidence. — from egotism
Conceit is somewhat stronger than self-conceit. — from pride
Self-conceit is ridiculous; conceit is offensive. — from pride