Picture a lifted to the mouth, and then the mouth refusing it. The tongue and the roof of the mouth say no, the head turns a little, and the spoon comes back down. That moment of not being able to swallow is the whole word. Sometimes what is on the spoon is real food. Sometimes it is a fact somebody is trying to make you take, and the refusal feels exactly the same.
From the word’s history
Our Wiktionary evidence builds the word from un-, plus palate, which comes through Old French palat from Latin palatum, the roof of the mouth, plus the ending -able. So it literally says 'cannot be taken by the mouth', and the modern figurative use is that same refusal moved from food to facts.
手上的 Wiktionary 資料把這個字拆成三塊：un-（不）、palate（上顎、味覺，經古法語 palat 來自拉丁文 palātum）、-able（可以…的）。所以它字面上就是「嘴巴收不下的」。今天的比喻用法，可以想成同一個拒絕的動作，從食物換到了事實上。
Wiktionary, "unpalatable"
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