In it's definition, anything that's animated is considered Anime (including cartoons, ex; Ben 10, Looney Toons, etc)
That's how Japan views it, we (the west) view it and define it as something that comes strictly from Japan.
Last Airbender, Korra are what I consider American anime. (RWBY is widely accepted to be anime).
Only reason why this debate exists is simply because people believe Japan will lose part of it's cultural identity if we were to accept Non-Japanese animations as anime.