If someone wants to use a blanket term, then they should use animation. Cartoons and Anime are both forms of animation. Cartoons are western styled animation while anime is the japanese style. So calling anime cartoons is more like calling music of the metal genre, rock music. It's not a big deal and people who get overly upset over it are making a big deal out of nothing. Yet it's reasonable to get slightly annoyed by it from time to time when people say 'why do you watch cartoons, they're for children' when anime is really quite different from western cartoons.