Furries are boring. Basically just Xenos that can't be mustered to break from preconceived notions and mainstream sensibilities. Pfff, I say to them. Pfffffft. If you need more evidence, just look at how fast the furry fandom jumped all over pokemon. Basically, it's a fandom characterized by a serious dearth of creativity.
On the other hand, I love the idea of non-humanoid intelligent creatures, the potential for animal traits to bring in a wide variety of preconceptions to bear, either to support a character design, or to mislead in preparation for a subversion. I'm fascinated by the idea of both human extremes as norms (which is what much of the spectrum classified as "furry" is, more or less, in disguise), and the narrative potential of role-playing beings that are intelligent but not-quite-human in some fundamental way. I like making use of the historical cultural associations humans have created for animals, playing with those tropes to guide and twist expectations, and the large works of mythology and important literature and cultural milestones that have made heavy use of this history. I'm fascinated by costume design, especially masks, both in terms of mechanical construction and in altering the face one displays the ability it has to fundamentally change many social interactions in ways you wouldn't quite expect. I especially love the sense of play that seems to be a central component to a lot of furryesque concepts, the feeling of dwelling in a place of imagination where boundaries are less clearly defined and the possibilities not so mundane.
So I can fully understand the appeal of the furry fandom as a whole, where it comes from and why it exists, and there's quite a lot to it that I'm more than happy to involve myself in. But overall, I find it (much like the anime fandom in many places) lazy and unambitious - to intent on coasting on it's own norms and inertia to really break new ground in interesting ways, and too keen to be happy with knockoffs and derivative works that do nothing but take away from the original. This doesn't mean there are plenty of examples of quality furry work - anthropomorphic humanoids have a long history of being powerful tools for much the same reason I explained above. But, just like in computer science, something being a good tool with many interesting possibilities doesn't really make the fandom that tends to spring up around it any less tiresome.
When you start supplanting your identity with conceptual or group loyalty, you've got issues, whether it's defining yourself as a furry, a Ruby fanatic, a homestuck, a Democrat or a teabagger.
So do I like a lot of furry stuff? Yes, I do. Do I consider myself a furry? No. As a label, that's constraining, confining, and inaccurate.