Having rolled a few fags in my backyard in my day, I understand completely.
Just have to understand that, unless one is a Brit, a fag and a faggot aren't the same thing.
Thought I once heard fag used in British English (perhaps obsolete) referring to someone who was one's chum in one of those all-male British "Public Schools" (= "Private Schools"). And I didn't get the impression at the time I saw it that there was any sexual connotation.
Also, I know I've seen faggots used to describe a bunch of sticks or kindling or similar.
I wonder if these usages led indirectly to the common meanings for these words as we know them today? I can see how a word for a close friend in an all-male school might eventually morph into some other meaning. But as far as the sticks go ..... no! I won't go there!