Picture a baby who cannot talk yet — the stage the word was built on. Medical writing still uses it exactly that way, as a label for that period of life. The other route takes the same picture and lays it over a grown person: an adult doing what only that stage would explain. Nothing about the picture changes; what changes is that it is now in the wrong place, and that gap is the insult.
From the word’s history
From Latin infans, a child who does not speak yet, plus -ile, meaning belonging to. So the word first meant simply of infants. The dictionary record dates the pertaining to infants use to the mid-15th century and the critical infant-like use to 1772, which is why the technical meaning is the older, more literal one.
來自拉丁文 infans（還不會說話的小孩）加上字尾 -ile（跟…有關的），所以它最早就只是「嬰幼兒的」。詞典紀錄把「跟嬰幼兒有關」放在十五世紀中，把「像小孩一樣」這個帶批評的用法放在 1772 年。也就是說，專業的那個意思才是比較老、比較字面的一邊。
Wiktionary etymology supplied in this evidence packet (source_ref kaikki:3f6f69a190036ae4:1139163449): Mid-15th century, pertaining to infants, from Latin infantilis, equivalent to infant + -ile, from infans. Sense of infant-like is from 1772.
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