I’m curious about this, because by definition, the American Civil War was a “civil war” (emphasis mine):
A civil war is a war between organized groups within the same state (or country). The aim of one side may be to take control of the country or a region, to achieve independence for a region, or to change government policies.
Those who don’t like calling it a “civil war” believe that the Confederacy actually became a legitimate separate country during that time, therefore it doesn’t count. It’s a mainly academic argument, until you realize that the reason they persist in calling it something else is that they think it’s still a separate country and that the Union is an illegal and illegitimate occupation force.
You can, of course, imagine the other stuff they also believe.