Hrmm. Well, the largest problem with coming up with new terminology, is making it relevant enough for the general public to use. The main problem being, that most people don't understand even the most basic parts of the relationship between sex and gender. Until they are able to understand them as separate concepts, coming up with viable new terms that are meaningful is going to be difficult. It's the same sort of problem you get with the alternate pronouns (hir, zie, etc...) They're certainly viable words, they're generally short and simple combinations of current gendered pronouns...but they don't have much meaning outside of certain websites or internet based groups. In the context to which you're referring (creating new words for broad social usage), such new terminology doesn't mean much when the public is unable to apply it.
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Some of this is going to take time. Time for society to change their biased and incorrect philosophy on the matter of sex and gender. As with races years ago..."Negroid" "Mongoloid" These are ways that society used to classify races, often reflecting their prejudice. (ie. "Mongoloid" was long associated with down syndrome).
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Negative stigma: This is a big one.
I honestly think that these issues being included in the DSM does not help us. Classifying a group as "mentally disordered" greatly stigmatizes them. We can create all the new terms we like, but as long as those terms are associated with "mentally disordered," it's going to be difficult to create the fresh new meaning that you're looking for.
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Ok...enough with the naysaying and difficulties. What can we do?
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If we take a page from different races, we would be looking to find a different wording that physically describes us or where we came from. (Black, Negro, African-American etc) If we do this, we're pretty much confined to "sex", "gender" and their synonyms or variations thereof. As society often confuses sex and gender, if they even realize that there is a difference...along with the stigma that sexual topics carry in this society, this probably isn't the best way to coin a new term.
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If we take a page from gays, we would be looking to co-opt a word that relates positive imagery, but doesn't focus on the matter at hand within its verbiage. (ie. gay used to only mean "happy, flambouant, etc 100 years ago. Today, people generally don't use it that way without first considering its dual meaning.)
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For things that often can't be overtly seen like sexual preference or gender identity, this may be a better way to go. But then the question is...what term to use?
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And here enters the difficulty of having such a broad community to define.
"Transgender": Whether it be about overt sexual markers (from clothing concerns and adornment to self image and body image) or about matters of mental/emotional expression, it's a vast and varied group of people to attempt to define within one word...while relating any meaning with that word other than "different from the norm." I think Transgender works well for now in that rather broad capacity...though it's about as specific as saying "people" with all of the variation contained within that community.
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Part of the problem is how we currently look at the community, when we define the smaller Trans-sub-groups. Often, we're defining based upon intent or motivation, which isn't something you can see...and, unlike homosexuality, the origin isn't seen as a constant within the sub-groups. This makes creating acceptable words for the sub-groups more difficult.
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In short:
When someone says "I'm gay." We don't ask..."how are you gay?" It's understood: "Oh, so you like men. Got it."
When someone says "I'm trans." It's not so cut-and-dry.
I'm dressed as a man/woman (or something else society can see)...
...because I am one.
...because I was born with a birth defect.
...because it better reflects my gender.
...because I don't agree/identify with this society's rigid stereotypes.
...because I'm not a man/woman, but something else.
...because it makes me feel comfortable/relaxed.
...because it makes me feel horny.
...because its forbidden, and gives me a rush.
...because I think it's a lark/fun.
...because I'm a performer.
...etc...etc...etc...
To bring to quick summation, there really isn't any way to make a single word for all of trans individuals that will bring the clarity of meaning that is desired. Unlike the relatively simplistic subjects that define "gay" or "black", it's just too varied of a group if we follow the current philosophy of delineating that group based upon intent/motivation. (Perhaps we shouldn't?)
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So...lets look at a specific subgroup (my own): transsexual.
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Personally, I don't care for the term. Just as metrosexual has nothing to do with sexuality, transsexual is likewise misleading.
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How to define the group though?
Some only want to be seen as men/women. Any term at all, no matter how benign, would identify them as something else.
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Trans? = In between or Changing. While perhaps accurate, "in-between" is something that many don't want to be seen as. Perhaps more because of the lack of social acceptance, rather than the simple act of being.
Dual? = Both. Accurate in some respects, but misleading in others...especially with the general ignorance about the relation of the subjects of sex and gender.
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I imagine that the term "gay" could have arose from watching 'flaming' effeminate gay men. If you've ever had a gay friend like this, you know exactly what I'm talking about. (Obviously it wouldn't work as well for all gay men, but I digress) I can't think of a word that would sum up a large amount of transsexuals though, as even within that subgroup our experiences..and temperament...vary widely. Some have arrived at a place that they are finally comfortable...while others are either just beginning, or on their way toward the same. 'Gender refugee' doesn't quite float my boat though.

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Hrmm...still haven't gotten very far with coming up with a new name though. It is a difficult quesiton.
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Currently, I tend to prefer "Transgender" over transsexual or other similar terms. Even if I have to explain what I mean, the term....to me...is not quite as misleading.