Why are Cigarettes called fags?

It seems that it originates in a term used in sailing, or shipping. In ship or sailor terms, a "Fag-end" was a rope that was frayed and useless at the end. Cigarettes have a non-smokable butt (or filter) on one end that is useless, so the term "Fag" got applied to the butts, and ended up being used for the whole of the cigarette. The Word "fag" is a British term, used to describe a tobacco cigarette. * The term "fag" is also short for Middle English "Fagge," or to droop. A fag is a student at a British public school who is also required to perform menial tasks for a student in a higher class.

* In British English, it means to drudge or do fatiguing or tedious work.

As previously stated, it means a cigarette and is short for the term "fag end," which means the butt of a cigarette. And it also means the last and worst part, the frayed end of a length of cloth or rope, an inferior or worn-out remnant or a broken thread in cloth, something that hangs loose. See the Related Link for verification.
Cigarettes are only called fags in the United Kingdom. In the United States, they are not called fags . Fags is just a slang term that is used in the UK.