There are several urban-legend false etymologies postulating an acronymic origin for the word.
None of these acronyms was ever recorded before the 1960s, according to the authoritative lexicographical work The F-Word, and thus are backronyms.
These roots, even if cognates, are not the original Indo-European word for to copulate, but Wayland Young argues that they derive from the Indo-European *bug– ("be", "become"), or as causative "create" [see Young, 1964].
The Oxford English Dictionary states that the ultimate etymology is uncertain, but that the word is "probably cognate" with a number of Germanic words with meanings involving striking, rubbing, and having sex or is derivative of the Old French word that meant "to fuck". Paul Booth claimed to have found "(possibly) the earliest known use of the word 'fuck' that clearly has a sexual connotation": in English court records of 1310–11, a man local to Chester is referred to as "Roger Fuckebythenavele", probably a nickname.
"Either this refers to an inexperienced copulator, referring to someone trying to have sex with the navel, or it's a rather extravagant explanation for a dimwit, someone so stupid they think this that is the way to have sex," says Booth.
There is a theory that fuck is most likely derived from Flemish, German, or Dutch roots, and is probably not derived from an Old English root.
There may be a kinship with the Latin futuere (futuo), a verb with almost exactly the same meaning as the English verb "to fuck".
During the Black Death in the Middle Ages, towns were trying to control populations and their interactions.