Give them like hardcore research on Gender Dysphoria that can explain WHY you are doing it. Look for articles that are more objective than subjective (fact rather than personal feeling- because we'll get to the subjective (personal) in a moment). And there are many different resources that you can use. Talk to your gender therapist/ psychotherapist because they can be a GREAT place of information for you. They can appoint you to local resources to find information to give to them; pamphlets, reading material studies, and overall general information on both Gender Dysphoria and Transgender/ Transition.
Now for the subjective part;
I had to deal with this from my dad, he was a real a$$butt about the whole thing (yes that was a Supernatural ref). But you
CANT expect them to come around over night. It takes time to process and digest. And you might have to answer some really awkward questions, then again you might not.
SO! without further ado the subjective/ personal feeling part; What I did is sat down and thought "Why am I transitioning, what do I personally feel? How do I explain this all to someone who cannot and will not understand?" (trust me it's easier than it sounds).
Then I outlined all things that came to my mind, I just wrote everything down. A few basics for me were "Feeling uncomfortable in my own body, felt awkward looking in the mirror, couldnt face myself in day to day life." And a whole bunch of other DEEP rooted, and deep meainingful things.
Then I sat down put them in a flowing order, and wrote an essay to read to them that explains EXACTLY what was going on, what I felt, WHY I felt that way.
It wont be easy, because you do need to look into yourself here. You need to first understand yourself before THEY can understand you. And trust me this can be VERY therapeutic