Generally speaking anyone on any side of any issue who really really "wants to debate you" isn't actually searching for information. They want to debate you because they feel they've already won, so nothing you say will change their minds.
When it comes to people being anti trans, the vast majority will fall within at least one of two camps:
1) "Trans people are icky, and they force me to think of things I don't want to think about." This is the largest group, and it mainly stems from lack of knowledge. There was a lot of this around the gay community in the '80s and '90s. The main way to combat this is to be yourself and a good person. Once people realize we're not trying to recruit their children or trick them into bed with us it will subside.
2) "Acknowledging a transwoman as a woman (or vice versa) is a denial of objective reality, I will not take part in a lie." This one is a little harder, and is where a lot of self doubt comes in. It's important to remember that within western civilization a lot of the intellectual infrastructure revolves around the promotion and restriction of communism. One of the ways that communist societies function is to constantly redefine reality. A good example of this is the previous ruler of North Korea, Kim Jong Il, having his subjects talk about how he hit 11 holes in one on his first game of golf. Such a thing is absurd, by forcing people to repeat an obvious absurdity he was exerting power over them. This is where the whole concept of "the LGBT Agenda" comes from. They feel that calling you a woman when they can lift up your skirt and see that you're what they feel to be a man is further proof of this.
This can cause a lot of problems because they'll seize on "I identify as female" as proof of how silly it all is. These types are hard to engage with because they'll just twist any statement to fit their preconceived notions. The only thing I can think of is to say that trans people are trying to use metaphors and similes to explain a feeling that's hard to understand if you don't have it, and hope it sinks in.
3) There are some people who feel that they have the entire world completely figured out, to the point where it becomes an integral part of their identity. If that worldview doesn't include trans people then it just must not be a real thing.
As to the actual studies you have to look at the actual age of the studies as well, if you go back to the '60s and '70s there were people who weren't trans who were undergoing SRS. Also until T-blockers were developed you were expected to transition and undergo SRS fairly rapidly since the very large doses of Estrogen were considered dangerous. Hence it was a bit of a leap of faith in those days since you couldn't be sure of how you'd feel until you were done.
In all honesty there's really only been good science on the subject for the past 10 years or so.
