A furry has two definitions. On one hand it's people who are part of the furry fandom, the global community of fans who love and appreciate anthropomorphic cartoon animal characters and their artists. On the other hand, those anthro animal characters are also called furries. And not all such characters have fur, such as bird characters (featheries), reptilian and dragon characters (scalies), aquatic characters, etc.
It's debatable whether a minotaur would be considered a furry, since it's described as a man with a bull's head rather than a bull with a human-shaped body. A dragon could be considered a furry since they usually have at least human-like thought and speech. I don't think furries in the furry fandom would consider a faun to be a furry since it's a man whose lower half is a goat. Such a character might be more considered to be zoomorphic (a human with animal characteristics) rather than anthropomorphic (an animal with human characteristics). And Star Wars characters...for those who clearly don't look human, I suppose they *could* be technically considered furries since they are nonhuman species with human-like characteristics, but generally furries don't consider Star Wars characters to be furries. I don't even know of anyone who calls Chewbacca and the Ewoks furries.
Anyway, since you're not intending your costumes to be fursuits, you don't have to call them furry. Your friend apparently does consider them to be furry. It's just a matter of differing opinions. Ask him to please stop calling them furry since you find it annoying, but if he doesn't stop, just ignore it as something entirely insignificant.
BTW, Jeff there doesn't seem to know what a furry is either. Furries do not wear their fursuits "almost constantly" and are not obsessed with their costumes (those who have them). Fursuits are very expensive and most furries have only one which they wear with great pride. But considering how uncomfortable they are to wear for any real length of time (it takes dedication to wear one) and how difficult they are to clean and repair, nobody is going to wear one "almost constantly".
furry since 1999, active in the furry community since 2008