Origins
Neutral is a grammar term that escaped into politics. Latin neuter combines ne- ('not') with uter ('either of two'), producing 'neither one nor the other'. It was coined to classify nouns that were neither masculine nor feminine.
The grammatical sense came first by over a thousand years. Latin grammarians needed a word for the third gender — the one that was neither he nor she. Neuter filled that role. The adjective neutrālis, 'of neuter gender', appeared in late Latin grammar.
The political leap happened in the 15th century. Diplomats took the grammatical concept — belonging to neither side — and applied it to states that refused to take sides in war. The metaphor was precise: just as a neuter noun belongs to neither masculine nor feminine, a neutral nation belongs to neither belligerent.
Development
Switzerland formalised its neutrality after the Battle of Marignano in 1515, around the time the word was gaining its political sense in English. The coincidence is not accidental — the concept and the word evolved together.
Science adopted the word repeatedly. A neutral solution is neither acidic nor alkaline. The neutron, discovered by James Chadwick in 1932, carries neither positive nor negative charge — it is the neuter particle. A car in neutral is engaged with neither forward nor reverse.
The word's journey from Latin grammar textbooks to United Nations resolutions is a study in how abstract categories become political realities.