Okay and now how about some art that's not meant to be sexualized in any way at all?
The one twist there is that a lot of people will say something that's meant to look cute or appealing in an adult way is "sexualized". See: any picture of a female anthro animal ever that has anything resembling boobs, even if the character is dressed like a nun head to toe.
I guess a good general definition of furry is; "People who are fans of anthropomorphic animals"?
The term for "furry" was coined around 1989 among comic book artists who were drawing anthro animals for adults - note that means stuff like Yojimbo, as well as "adult" in any kind of cheesecake sense. Ironically, one of the original reasons so many artists began making grown up anthro characters was to break out, and for variety - it was simply more interesting than trying to be the 100th guy drawing Wolverine to get a job at Marvel Comics. And many of the indie comics at the time, were just imitations of big-name comics, so didn't stand out. One could say stuff like TMNT was a precursor to the minor explosion of anthro animal art and comics in the US, especially on the west coast.
The general definition of furry still remains, people who are fans of anthro. That's about it. Originally, for a few years, there was the term "furry lifestyler" which was used non-ironically to denote someone who had a personal anthro persona and was into the furry "scene" as a Star Trek geek might be a full time Trek convention goer. As with any group, there was controversy and debate over just what the difference really was.
With the huge influx of young people thanks to the Internet spreading the furry meme, I don't think "lifestyler" is used much anymore except in small pools of fandom culture. Most people haven't even heard of it.
One reason why you see controversy whenever "furry" gets mentioned on the Internet, is the early 2000s Internet shock culture like Something Awful did a great job of spreading the meme that "furry" denoted, exclusively, people who make anthro animal costumes and have sex in them. That's it. Or, it denoted, exclusively, people who practiced beastiality on farm animals or pets. Their anthro characters online wuz the secret code they used to hook up!
A few folks in the thread brought up the "why are furries so defensive" thing, which, has always been a bit of misdirection because it's usually phrased as a loaded question: "why are furries so defensive about their *fetish* when other *fetish* groups hide in shame..." One shouldn't have to explain what a ridiculously fallacious line of reasoning that is, but... furry fans in the primary fandom have a reputation for freaking out. And it's true. But if you stop and consider what's behind it, there is a genuine point of contention. A lot of furry fans protest because they flack pitched at them assumes that liking anthro characters (of any kind) is itself a sexual fetish. If the furry fandom was in reality its stereotype, it ironically would probably do better. It could go hook up with the other adult sensual/sexual hobbies like BDSM and find some solidarity. The problem, ironically, arises from the fact that despite all of its problems, the fandom as a group is too complex for what it is typically dismissed as.
I actually have understanding for people who think that the furries are exclusively a group of fringe fetish fans, because the fandom, as an organization, is pretty unbalanced in the current era IMHO. On one hand, adult should not give a flying frack what other adults' fun buttons are, and people are too sheltered and uptight about stuff like that. On the other hand, when the largest online communites and cultural epicenters for the American furry fandom are largely porn sites that is steeped deeply in fetish culture, yet there's so many people who would consider themselves furries/anthro fans that are interested in much more than just that... there is a deep imbalance.
It is a reason why I suspect we're going to see something else, and more broad, assimilate what people think of as the furry culture over the next few years. The hard truth is that during the furry internet explosion, a lot of the kids who joined up where, statistically speaking, likely to have already been fringe lurkers and a lot of them had problems. Some actually used furry to get better, having found a way to socialize. Others, well, didn't do so hot. But, as an interested observer, I have noticed over the last couple years, with a much larger portion of the population online, folks who discover anthro stuff and go "hey, I kind of like it" are coming from a wider pool of personalities. It's actually an optimistic trend. They're also bringing more actual talent to the subculture, so the quality of furry media is in fact, going up.
While I'm typing too much, I will say one thing about that last angle, the media: furry has a reputation for creating and promoting terrible art, and there is a specific reason for that: until recently, the primary motivation of furry fans was simply to create content that served the purpose of displaying something anthro. This is not really different from any kind of fan art, at the root. Fans who make stuff just want to see their dream object made real, they don't necessarily have any aspiration to be good at it. So fans are far more forgiving of a piece of art that's technically poor, if it highlights their favorite subject (or obsession). What outsiders often don't get about the furry fans, is that the fandom is heavily "do it yourself". It is largely about content creation, and there's a huge push to make stuff rather than just consume. The downside is that during its internet explosion stage, it had no standards. Furries just wanted to see anthro animals at any cost, because such characters oriented at adults - even in a non sexual way - were rare in media. So the fandom developed a culture of rewarding people for making any kind of art (or writing) period.
That is actually changing too, though slowly. There are a lot of people who either already have real ability when they show up, or existing fans who want to get good.