Loath adj. disinclined; not willing to take an action.
Loathe v. to violently dislike; to hate.
Words in the Wild: Though he loathed heights, he was loath to back out of his skydiving lesson.
If you follow the link to loath in Merriam-Webster online, you’ll see that it offers loathe as a third spelling variant after loth. CanOx and OED agree, however, that loath is the first spelling, loth is the second, and neither offers a third.
Interestingly Merriam-Webster’s definition of loathe doesn’t include “disinclined,” suggesting that the word shouldn’t really be used in this way. Perhaps its inclusion as a third spelling variant of loath is due to its widespread misuse.
It definitely seems safest here to stick to the agreed upon first spellings of these words, shared by all three dictionaries.
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