Loath vs. Loathe

Loath is an adjective meaning “reluctant” and should be followed by an infinitive (verb form with to):

loath to take on such a huge project (reluctant)

Loathe is a verb meaning “to detest” and should be followed by a noun or pronoun acting as its object:

loathe his trite, rambling speeches

loathe listening to his speeches

In the last example above, listening is a gerund, an “-ing verb” acting as a noun.