Loath means very unwilling to do something. You will do it, and every part of you objects.
It always takes to and a verb: loath to admit it, loath to interfere. That construction is the only place the word appears. The real difficulty is the neighbouring word loathe, with an e, which is a verb meaning to hate intensely, and mixing them up is one of the commonest slips in written English. Loath is an adjective and loathe is a verb, and that is the whole distinction.
1adjectiveloathVery unwilling to do something.
“I am loath to disturb him at this hour.”
Loath was once much stronger. Old English lāð meant evil or loathsome, the same word that gives loathe, so being loath to do a thing is a worn-down form of hating it.
Proto-Indo-European
*h₂leyt- — to do something abhorrent or hateful
Proto-Germanic
*laiþaz — loath; hostile; sad, sorry
Old Norse
leið
Old English
lāð
Middle English
lōth — loath; averse, hateful
English, today
loath
Built from
From Middle English lōth (“loath; averse, hateful”), from Old English lāð, lāþ (“evil; loathsome”), or Old Norse leið, leiðr (“uncomfortable; tired”) from Proto-Germanic laiþaz (“loath; hostile; sad, sorry”), ultimately from Proto-Indo-European h₂leyt- (“to do something abhorrent or hateful”). The word is cognate with Danish led (“disgusting, loathsome; nasty”), Dutch leed (“sad; (Belgium) angry”), French laid (“ugly; morally corrupt”), Catalan lleig (“ugly”), Icelandic leiður (“annoyed, vexed; sad; (archaic or poetic) annoying, wearisome”), Italian laido (“filthy, foul; obscene”), Old Frisian leed, Old High German leid (Middle High German leit, modern German leid (“uncomfortable”), Leid (“grief, sorrow, woe; affliction, suffering; harm, injury; wrong”)), Old Saxon lêð, lēth (“evil person or thing”), Swedish led (“bored; tired; (archaic) disgusting, loathsome; evil”).
Etymology from Wiktionary, CC BY-SA