My definition of a self-centered person is one who is selfish and inconsiderate. Here's the dictionary's!

Self-centered

Engrossed in oneself and one's own affairs; selfish.

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Selfish

Caring supremely or unduly for one's self; regarding one's own comfort, advantage, etc., in disregard, or at the expense, of those of others. "They judge of things according to their own private appetites and selfish passions.

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Inconsiderate 1:  careless of the rights or feelings of others

(Examples coming soon)