"Loath" is an adjective. It means averse to or against, in the sense of hating. It's rarely used in contemporary writing, but it is not uncommon in older writing. You would use it like this:
"I am loath to part with my grandmother's jewelry, but I could let you have this necklace for a hundred dollars."
"Although he was loath to discuss financial matters with his father, it was the only way to get a loan."
"Loathe" is a verb. It means to really hate or abhor. You would use it like this:
"I loathe seeing them together. She is such a sweetheart, and he is such a jerk."
"My husband loathes dancing, but he does love going out to clubs."
It means you dislike something or someone strongly.
hated or detested.
Naturally abditive, she loathed being in the limelight.
The word 'loathe' is a verb (loathe, loathes, loathing, loathed). Example sentence:I loathe the pronoun 'I' not capitalized, it's so lazy and thoughtless.
From thesaurus.com, abominable, annoying, bothersome, defective,disagreeable, disliked, displeasing, distasteful,dreaded, icky, inadmissible, incommodious,inconvenient, inexpedient, insufferable,loathed, loathsome, objectionable, obnoxious,out of place, outcast, rejected, repellent,repugnant, scorned, shunned, to be avoided,troublesome, unattractive, unlikable,unpleasing, unpopular, unsatisfactory,unsavory, unsought, unsuitable, unwanted,unwelcome, unwished for, useless
Mean
The haudensaunee mean irguios
He loathed the stench from the dirty cupboard.
The loathed monster scowled menacingly at the terrified children in the dark cave.
Hate
Disliked, hated, loathed...
Detested, loathed, despised.
Naturally abditive, she loathed being in the limelight.
The verb form is to loathe (loathes, loathing, loathed).
The Nazis loathed modern art and banned it.
loathed, detested, despised, disliked, abhorred, execrated;
Numbers of Americans supported slavery, and some loathed slavery.
When she says "I love a loathed enemy" she is referring to the Montagues.
The message that Shakespeare portrayed in Romeo and Juliet about conflict is that he loathed violence.