The terms "werewolf" and "were" really bug me. It brings up ideas of physical shapeshifters and horror movies and roleplayers and thus should not be associated with Otherkin and therianthropy in my opinion. It makes me less inclined to believe someone who claims to be a werewolf over calling themselves a wolf therian. It's just one of those words that just rubs me the wrong way and I have to fight to take someone who calls themselves a "werewolf" seriously. (No offense meant to anyone here, it's just my initial reaction to the term!)
However since I haven't seen the term lycanthropy used by therians, that term doesn't bother me as much. I don't think it should be associated with therians because it is in fact a medical disorder. Last time I checked "therianthropy" and "Otherkin" were not classified as medical disorders or diseases. That and if wolves get a special "-anthropy" I would think all the other types of therians would want a special title too. <!-- s:roll: --><img src="{SMILIES_PATH}/icon_rolleyes.gif" alt=":roll:" title="Rolling Eyes" /><!-- s:roll: --> And the more terms there are, the more confusing it tends to get!
A few therians in the community prefer to call themselves "animal people" because they (at least from what I've seen) consider the term "therianthopy" to be for newbies and they dislike the therian community as a whole (probably for all the bickering over terms!) and don't want to be associated with it. I don't have a preference either way. After my initial awakening, I was introduced to the term therianthropy before anything else, so that's what I use. It's only been over the past 2 years that I've heard the term "animal people" so while I would use both terms interchangably, I'm more inclined to use "therianthropy" because that's what I learned first. I think in most cases, the first term someone learns to descibe themselves is usually what they end up using.
It also bothers me when some therians insist that therianthropy is not grouped under the term Otherkin because therians are "real" animals while Otherkin tend to be fantastical creatures and species out of legends. Sorry, but believing that your soul is something other than human puts you under the Otherkin umbrella. <!-- s

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And as far as the dragoness/dragon term goes, I think that's similar to how some people prefer actress to actor or firefighter to fireman, etc. Politically correct and all that! I'm an actor and I'm female so that would technically make me an actress, but I just use the term actor as that's the actual name for what I do. In my case I'm a wolf, and even though I'm female, I don't call myself a wolfess. Some people may prefer the gender specific terms, but I don't particularly care either way.