Harmonica

Where did the term fag come from?  I understand that in other countries a fag is a cigarette.  Is it because we suck on a cigarette for the smoke within?  Something about sucking on that small stick that translates to sucking on a dick? 

In all reality that would mean that homosexuals could also be called straws or harmonicas.  I think fag is just a fun word and people were looking for an excuse to use it more, like the word teat.  People liked it so it became tit, which is now a playful word for breast.  I’m sorry harmonicas.