What even is this? Not the contents of your screenshot, but your misplaced belief that this is somehow an incorrect mode of speech. Please tell us you haven't read many novels without telling us you haven't read many novels. The grammatically correct usage would be "be loath", because the ending 'e' is the difference between an adjective and a verb, but the ending e is a common stylistic choice in literature. I doubt, however, this is the contention you have with it; much more likely is the case of you merely being unacquainted with the phrase as a result of being unread.

If I may, "I would be loath to..." is a phrase, if an archaic one. It is definitely uncommon, but I wouldn't say it is wrong by any means. Actually, it gives a creative flare to the character more than simply saying, "I would hate to be interrupted."

How to English 101