“Loath” (sometimes “loth”) is an adjective meaning “reluctant.” It rhymes with “both.”
“Loathe” is a verb, meaning “detest.” It rhymes with “clothe.”
This is a useful distinction, and in danger of being lost.
The often-heard formula “X is loathe to do Y” is a ticketable offense. If caught, you will get two points on your poetic license and will have to go to language school.