Like it or not, you're asking people to do something for you that the vast majority of people know nothing about, let alone understand. We live in a gendered society, and in general, a gendered world--asking to add in a third gender is a lot to ask--not because you don't deserve the respect to be addressed the way you feel you should be addressed, and not because there's anything necessarily wrong with it; it's simply not the way our language is constructed, not the way our culture is constructed, and it might feel awkward or forced for others even to try to refer to you with the pronouns you prefer, because that's just not the way we are used to talking or thinking. If you insist upon going against something that is so ingrained in our world, you have to have a tough skin. Some people will be confused, some people will be offended, some people will roll their eyes--don't let it get to you, and don't get too offended. People will have questions. They will be certainly be personal question. Your best bet, if you don't want to come off as some nitpicky PC militant with an agenda to deconstruct male and female identity, is to be positive, be informative, and be happy about other people's inquisitiveness. And if someone gets offended and blows you off? Shrug it off and walk away; you don't have to deal with them, and you should pick your battles wisely.

If it is someone you have to deal with in your life, and you can't just shrug their hostility off, that's trickier, and would depend on the circumstances. As for your therapist, I think that perhaps you aren't getting the point--I think she was asking you how you might feel about people referring to you in one way when interacting with you, because it's what you would like, and people referring to you as "he" or "she" when you're not around, because that's just the way our minds work. Perhaps she was asking, why does a generic, made-up gender label mean so much to you, linguistically? Does it bother you, or matter to you that people are probably not thinking of you in this third gender category in their perception of you, but will refer to you differently when you're not around in order to prevent offense? Why do the labels matter to you? I think she was challenging you to see your reaction and to get your insight into why it matters to you, not because she think you're ridiculous. She's a therapist; she's going to challenge your thoughts, emotions, perceptions and behavior--we would never get any insight into ourselves without the challenges that other people approaches us with when it comes to explaining ourselves. It's how she gets to know you, understand you, understand your thinking, and ultimately, how best to help and aid you.

I assume that you know why it matters to you, and you've thought about, dealt with many painful emotional trials that most of us don't have to worry about when it comes to our identity, and you've come to understand yourself in a way that you want to be conveyed to other people. So, tell it to your therapist, and see what she says. In the meantime, be thickskinned with other people (you just have to be--it will take practice, but don't let other people drag you down), and be armed with information and a good attitude. If you want people to warm up to what you ask of them, you need to know your stuff and be prepared to explain it, and you need to be nice about it--I can't tell you how many people I've met in the LGBT community who regularly miss their chance to do something positive for their cause, and take advantage of the opportunity to educate someone, because they were too busy being offended by their ignorance. A sanctimonious, self-righteous attitude is appealing to no one. A knowledgeable, friendly person who will take the time to answer your questions or explain themselves will usually get respect, at least for that.

Good luck!