word forming element indicating "oneself," also "automatic," from Old English use of self (pron.) in compounds, such as selfbana "suicide," selflice "self-love, pride, vanity, egotism," selfwill "free will."
1590s, "to concentrate at a center," from center (n.). Meaning "to rest as at a center" is from 1620s. Sports sense of "to hit toward the center" is from 1890. Related: Centered; centering. To be centered on is from 1713. In combinations, -centered is attested by 1958.
Others are reading
<a href="https://www.etymonline.com/word/self-centered">Etymology of self-centered by etymonline</a>
Harper, D. (n.d.). Etymology of self-centered. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/self-centered