What makes anime anime? I don't really know. What makes comedy comedy? SOmething thats funny. BUt what's funny. I don't know. What makes anime anime. TO me anime has a certain feel to it, you pick it up on the screen. IT looks different, it doesn't always look the same. (ONePiece, doesn't look like Ghost in the Shell, which doesn't look like FMA)> What I've always equated to as anime has never been based on what country it came from. But more for how the show presents it's story. A cartoon though a drawing that is animated always brings up a sort of farsical fantasy that is in no way presented in any sort of inteliigable way. It's funny and fun to watch, but is meant for kids. ANime to me has elements of fantasy, and science fiction. But beyond that it filters it through a world that is almost real. FMA presents some unreal themes, but the characters and what the two brothers are trying to accomplish are based on something that is very real. THe story of their search for a philosophers stone and their ability to do ALchemy is the icing on a very truthful look at 2 kids dealing with the loss of their parents. ANd Ed's struggle to fix what happened to his brother. It's rather hard to explain and I'm not really doing a great job of explaining it but, no matter how far out some of the particulars are in an anime show, they all seem to be grounded in some sort of real life situation.
The only other thing I can point out that makes an anime an anime and a cartoon a cartoon is character development. The animes I have watched have had 3 dimensional, fully fleshed out character. Say what you will but Bugs Bunny wasn't much more beyond taking out Elmer Fudd.