Simply, a furry who insists they aren't. Nottafurries will, for example: draw furry porn, write furry porn, commission furry artists to draw porn of them, have fursonas, draw art of themselves as their fursonas, go to furry cons, have extensive pages on furry websites, and have friends who are all furries. Yet they will get into endless, screaming debates with you if you call them a furry.
"After that rant he threw, I checked PrinceWolfSword's userpage. Fifty submissions; all Starfox porn. Total nottafurry."