If they were "offended" as you say, it was probably due to defending/taking pride in their hobby and wanting to better share the nuances of it that labelling it "merely a cartoon" glosses over.
I think one of the problems is that ?Anime? is a ready-used term that can help distinguish from the mindset of ?cartoons?. So why not use it? To refuse is like refusing to acknowledge that you can differentiate between a ?Van? and a ?Car?, they?re subtly different but essentially the same form of construction.
One of the problems is that people who don?t watch Anime as a hobby often have a very narrow view of it. They don?t take the time to study the industry, or are otherwise willing to be exposed to the knowledge, as it doesn?t interest them. Not everyone is like that but it leads to some assumptions.
"Anime" is not just about being an Animation to the Japanese. It?s an entire cultural industry and process that does cause a noticeable effect on the kinds of stories produced, compared to the western industry which is far more relaxed.
During the creation of a Manga/Anime story, it comes packaged with additional genres which will set the kind of story it may be by defining a target audience. Such genres are: Shonen, Shojo, Kodomo, Seinen, etc... Which target the typical tastes of different genders and age groups.
These are, of course, then in addition to genres such as Sci-Fi, Fantasy, Slice of Life, etc... And add categorical information to help you filter searches to something you might better enjoy.
One prevailing assumption with Anime, that I?ve come across, is due to most of the ?Anime? people saw growing up, on the TV before school, most probably fell into the Shonen genre exclusively. Which means it was aimed at young boys who're more into mindless action and progressively-stronger-battle stories (where there is always a bigger bad guy than the last).
Such examples are: Pokemon, Dragon Ball Z, Yu-Gi-Oh, Naruto, One Piece, etc... Alternatively there might be some Shojo, aimed at younger girls, but I don?t remember much of this.
People then form assumptions around these few examples and assume it speaks for "Anime" in general, because that?s all they?ve known, and so they then associate it with children when they grow out of such stories.
Another assumption is that all anime are long-running serializations: That they all have 200+ episodes like the above examples. A large majority of Anime though are around the ~25 episode mark, with many at ~13 episodes and a few at ~50. Those being entire, planned out stories that have a beginning, middle, and conclusion. Not a mindless assembly of continued contrivances. This is because a large majority of Anime start out as Manga, and have to essentially pass popularity (i.e. be good enough) to warrant an animated adaptation. Many Western Cartoons simply present a pilot episode and make episodes/seasons up as they go along, trying to cater to audience tastes at the time rather than a story that's liked fromt he start.
They acknowledge there are likely the occasional serious "gems" out there that deal with more complex storylines, but insist that so do western cartoons. The problem is they draw parallels where culturally there isn?t a direct connection. Most complex western cartoons are supplementary to an established franchise, or are a single movie, and are pretty limited. There are exceptions, such as Gargoyles, but they are by no means a popular market.
With Anime there is a whole genre or more to pick from; defined Anime that was written with a more intellectual, philosophical, or otherwise serious audience in mind, and doesn?t consider children whatsoever. Seinen is usually a good example of this.
Shows like Ghost in the Shell and Serial Experiments Lain are in no way comparable to shows like Beyblades and Bakumon, and so they?re defined separately.
It?s a hectic market too, and so there is more pressure for quality and creativity on Japanese Anime Writers than on Western Cartoon Writers, meaning there is often a stronger emphasis on story quality as a show is far more likely to be axed for being uninteresting if it?s not.
This approach to creation of Anime, with a broader market which is served sufficiently in most areas (compared to the west?s focus on children with shows such as Rocko?s Modern Life, Spongebob Squarepants, Catdog, Angry Beavers, etc...) means that it has an entire collection of content that you?ll never find in a western cartoon. When people say ?there?s an Anime for anybody? they usually mean that, so long as you?re open to watching the medium, there is most likely a story out there that specifically leaves a positive impression on you.
This is why people find the term ?Anime? useful, because it describes a different industry with a much different approach to storytelling than the western one. To abandon that term then abandons ?Seinen? and ?Shonen?, which is like abandoning ?Children?s Literature? and ?Adult?s Literature? simply because you don?t care for the distinction.
When ?Cartoons? develop a significant enough market in other age groups to warrant entire sub-genres which define age groups that shows are marketed at, then it might be a little more directly comparable. Until then though, ?Cartoons? are most often compared to ?Shonen/Shojo? with only a few, rare, outlying ones that appeal exclusively to more mature audiences; whilst ?Anime? caters to all. Also a few other, more minor factors, such as the humour/cultural themes being predominantly Japanese, and the artstyle often Manga. Those last bits aren't what defines "Anime" though, it's the different approach and resulting different content that does.
This is why I think it?s dismissive to lump ?Western Cartoons? and ?Anime? together simply under ?Cartoons? on the basis that they?re both ?Drawn Animation? and thus directly comparable. It just ignores the deeper industry behind everything.
