I'm own experience (being in the closet mostly, only told parents and some select friends) the main problem is that my being trans* forces them to define the concepts "male" and "female" for the very first time. People do not think about these concepts, they are taken as axioms (for lack of a better term). It's the first thing people ask after birth, it's so fundamental to our world view or mental map and more importantly it's wound up with a lot of complex social rules, cultural expectation: duties, rights and in the end, because gender is still unequal, privilege.
Everyone I told, had this moment where they had to think for the very first time every that the concept of gender might not be so simple. They don't have a problem so much with me, they love me and understand that this is hard on me. The problem is that they do not understand, and the very idea that gender might sometimes be a whole lot less simple, much more complex and ambiguous just doesn't "fit" in their map of the world. And anything that doesn't fit but can't be dismissed or ignored tends to trigger "taboo", "scary", "crazy" and in people so inclined "godless" or "demonic".
You really can't convince someone of anything as long as their view of reality depends on them not understanding it.
I don't think I can expect other people to adapt any faster then I did? I myself needed many years to figure out this weird conflict I had; Many more years to understand that it's much more then just being a man who it slightly more feminine. And years more to get to the point where I accept that I'm female and that this will never change. I know that I want nothing more then to transition.
For me the personal benefits are much greater then any personal cost. I am convinced that I can never be really happy as a man. That I will not be able to be myself as long as I have to keep pretending to be a man. The question however is more complex.
When the people I love are able to adjust then I will go ahead, and while they are not... I will be more myself, because I know that I can not continue to pretend or lie anymore. I will limit censuring myself and I will become more honest about my experiences, feelings, hopes, dreams, preferences, etc. Let them meet the real me and give them time to adjust to this shift in concepts.