The term "anime" itself isn't even meant to indicate a place of origin; it's an abbreviation of the Japanese word for "animation." This word origin is according to the Online Etymology Dictionary. Some claim the word comes from French, but the point remains the same; "anime" means "animation." In Japan, little, if any, distinction is made between Japanese animation and animation from abroad. "Anime" is used as a blanket term, the way Americans use "cartoon." The Japanese do not use the term in reference only to work from Japan and nor should Westerners.
It wouldn't seem correct to treat the entirety of any medium from any other culture with similar prejudice.
Unfortunately, this point tends to be ignored and most conversations about anime are cringe-inducing nightmares. It's not because of the fan-service and hyper-sexualization of young females often associated with cartoons from Japan, nor is it because of the sort of socially inept personalities commonly (if inaccurately) thought to exclusively enjoy the form. The conversations are often frustrating because at some point, at least once, someone will refer to anime as a "genre."
Okay, maybe - just maybe - anime does qualify as a genre in its own right, but as the term is currently used, meaning "from Japan," it's a genre the way "French film" is a genre. It's a genre the way "American TV" is a genre. It's a genre the way "PC games" or "internet videos" are genres. They're useful for describing "where," but not "what" and like each listed, anime needs qualifiers like "comedy" and "action" to clarify the label.
Yet Westerners rarely speak in such specific terms when referring to anime. In North America, anime as a form is so flattened by its own label, so homogenized by the nomenclature used in reference to it, that for most, it seems to be "all the same," and thus, far too easy for some to write off all at once. Our commonly understood definition of anime stifles the art.
It wouldn't seem correct to treat the entirety of any medium from any other culture with similar prejudice. We don't generalize all of British TV or Canadian webcomics. We don't lump together all of French music or Latin American food.
Yet many within the fandom insist on maintaining the very strict idea that anime is Japanese cartoons. Perhaps this zealot-like defense of anime's status quo grows out of a fear of change, or maybe it's born out of an intense infatuation with Japanese culture and the misguided belief that no other group could ever produce anime as well. Either way, holding to a definition of anime based on where it is created is harmful to the form because it is narrow and exclusionary.
Then again, perhaps anime fans deserve a bit more credit. It's possible the common definition of anime comes from a desire to avoid appropriating another culture's forms. Just as Americans have become sensitive to using imagery stolen from pre-colonial tribal nations as professional sports teams' logos, perhaps anime purists seek to preserve Japanese culture. The difference, of course, is that the ousting and exploitation of the many nations that existed in North America prior to European colonization is still a largely unresolved or ignored topic, whereas Japan has freely offered anime to the world.
Maintaining the dated and minimally useful definition of anime as "cartoons from Japan" seems suspiciously like snobbery and it's what keeps anime from achieving the mainstream credibility it deserves outside of legendary creators like Hayao Miazaki. It's what stops new creators from bringing new ideas to the community and most of all, it's what keeps anime purists from giving series produced in America a fair chance and beautiful cartoons like The Legend of Korra from reaching the widest possible audience.
Using the term "genre" when talking about anime could be acceptable, but only if it is established that anime is not necessarily content that comes only from Japan. Anime is a form defined by a common artistic style and visual language (just as one example, the use of chibi, which is Japanese slang that roughly translates to "cute" and within anime is a non-realistic style of animating characters used to emphasize moments of childlike behavior), a shared collection of tropes and themes, and perhaps most importantly, a similar canon of influences. And if this definition is accepted, then certainly anyone can make something in that style and The Legend of Korra is definitely anime.
Anime is more of a style than a genre. Within anime there are series and films for young and old, conservative and liberal, males, females, and anything in-between or outside. Anime includes comedy, action, horror, drama, and every other commonly referred-to genre in entertainment media. Why can't it also include "American" or "Western" as labels?