Think of someone standing in front of a throne and saying out loud, in front of everybody, that the seat is no longer theirs. Two things matter in that moment. The seat was theirs to begin with, so this is not walking away from someone else's job. And it is said openly, in front of witnesses, rather than done quietly overnight. The other meaning is the same moment moved off the throne and onto a duty: a job that was yours, publicly let go.
From the word’s history
The packet's Wiktionary entry traces the word to Latin abdicō, from ab ('away') plus dicō ('proclaim, declare'), first attested in English in 1532. So the word is literally 'to declare it away', which is why the public, formal act is still at the centre of both meanings.
評估資料裡的 Wiktionary 記的是拉丁文 abdicō，由 ab（離開）加上 dicō（宣告、公開說）組成，英文最早出現在一五三二年。字面上就是「公開宣告把它推開」，這也說明了為什麼兩個意思的核心都還是那個公開、正式的動作。
Wiktionary, "abdicate"
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