The root of this word is euphemism, ("the substitution of a frank expression that might offend or otherwise suggest something unpleasant to the audience, for a mild, inoffensive, relatively uncontroversial phrase.") with the suffix -oid, "indicating likeness, resemblance, or similarity."
A euphemoid has the appearance of a euphemism, but is not necessarily a euphemism. A euphemism is a polite way of saying something less polite. For example, one might say "I'm going to powder my nose" when excusing oneself to use the restroom (and restroom is a euphemism for toilet). In this example, a euphemoid would be if somebody excused herself to powder her nose, you would follow her to the restroom, and then find her actually applying powder to her nose. That would be an example of a euphemoid. Another one, though less likely, is if you went into a door marked "restroom", only to find people taking naps on cots. So far, my new word has limited applicability; but we're working on expanding the example base to make euphemoid into a more versatile household word.
The english language lacks gender-neutral pronouns. well, not really. We have he and she, and we also have it, but some people seem to think it only applies to lifeless inanimate objects. Nobody knows why this is so, but the belief that it cannot be used for a living human is so deeply ingrained in our culture, it can't be changed. Sure, it's fine for 80% of all english speakers to forget how to spell you're, but the word IT absolutely cannot be used correctly in gender-neutral situations in reference to humans. Maybe it's not PC enough or something. God forbid you call somebody an "it", or you refer to a potential she as a he! No no no, you have to fill up an entire page with a lengthy "he/she". It may be a lot, but at least you're letting the forward slash get a little literary action.
Anyway, assuming i explained that part sufficiently, we can get on with the words. Since one's gender is the first impression you get from somebody upon meeting, it's the first part of the word that is different. For example, with he and she, the difference is the H and SH at the beginning, but the E at the end remains the same. Therefore, the gender neutral he/she word is E.
Why E? why not? We already have two other one letter words, A and I, and two that sound like one letter words, O and U. E is the only one not used. another one letter word can't hurt. E is at the end of he and she, so it's already there. Who cares? Just use e as the gender-neutral pronoun. Come on, do it and get it over with. Your shortened sentences will thank you. It's not like we don't pronounce the H sound in he, because we do pronounce it. This is America, that's how we talk, we say the letter H. He and e will be easily distinguishable. Do you want to make a contraction with is, such as he's or she's? How about e's? You can do it with ease.
What about him and her? As I did in e, I take off the beginning of a word, and use the ending. But wait, him and her end differently. That's fine, I use the ending of both together, and formed mer. That's right, mer is the new gender-neutral pronoun replacing the cumbersome him/her. Want to make it possessive? just add an s at the end, for mers.
You might as well get used to these words now, because they're here to stay. Start using them today. What will your friend think? E will love it! E and mer will go right into mer vocabulary. And find a way to use euphemoid too, that one can have some very interesting applications.