Think of sympathy as a line that runs from one person to something outside them — and unsympathetic as that line failing to connect. Someone is standing there with their trouble, or with their plan, and nothing crosses over. Nobody has to shout or attack; the word only tells you that the warm line is not there. The three uses differ in what sits at the far end of the line — a suffering person, an idea, or a character in a book — and once in a book the line is drawn from us to them instead.
From the word’s history
Wiktionary gives the word simply as un- + sympathetic, with un- traced back through Middle and Old English to Proto-Germanic *un-. So the whole word is built by putting the not-prefix in front of an existing adjective.
Wiktionary 記載這個字就是 un- 加上 sympathetic；un- 這個表示「不」的字首，可以一路往上追到中古英文、古英文，再到原始日耳曼語的 *un-。也就是說，整個字是在一個現成的形容詞前面裝上「不」造出來的。
Wiktionary entry for unsympathetic, etymology tree (packet source_ref kaikki:3f6f69a190036ae4:986516448)
登入就可以看每一支怎麼連回核心畫面。