The term a cyclist is given when not part of or representing any cycling team or club. The unattached rider has no affiliation or outward allegiance to other racers or other teams. They are usually a small minority in amateur races. Little or no competitive advantage is lost or won in being an unattached rider since most amateur teams can not muster the required tactics to advance teammates in a competitive race.
Unattached riders are not found in the professional cycling ranks due to regulations, sponsorships and required support.
I think next year I'm gonna race Unattached, cuz this team is a bunch of (freds) and (dorks).