A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.
The actual answer is that "difficult" comes from "difficulty," which is itself from the French "difficulté." "Cult" is a direct shortening of the Latin "cultus."
If you ever really want to look at word origins, the Online Etymology Dictionary is great: https://www.etymonline.com/word/cult#etymonline_v_450
leaving a cult is difficult