Having worked with quite a few trans women, I am definitely open to a lot more evidence on both sides of the subject.
I'm highly disturbed by the pre-pubertal hormones we discussed a few pages back and I think there's a lot of merit in what you're saying - trans is being driven by societal desire rather than scientific analysis.
I have quite a lot of information if you're interested, although I'm not sure which aspects you're specifically talking about here.
You say 'both sides', and that indicates you might be talking about something other than what I thought you were. There is this widespread 'positioning' tactic, often employed in other woo beliefs, of pitting the idea one is a proponent of versus 'everything else' to create the illusion the proposed idea is on equal footing. This is seen in homeopathy vs 'alleopathy'. It's seen here in 'Blanchard's hypothesis' vs 'mainstream trans gender theory'. It also makes it simpler to straw man all of the science and debate on the subject to 'just about the feels' vs 'this science man's long really plus extra sciency words'.
At any rate, Blanchard's work and followers are one 'side' but the other 'side' actually are many competing theories and research that actually argue with each other on the details but don't even take his work as worth exploring. This is akin to evolution, just with a lot less data to work with. Specifically discrediting Blanchard isn't something most would even think to engage in because his work has simply bore no fruit to address predicatively. That said, his methods specifically have been taken apart and found not just lacking, but ridiculous.
For example, using his definition of 'autogyophile' and apply it to cis women results in 90%+ being categorized as 'autogynophiles', and a more rigorous application (stricter than Blanchard uses) resulting in almost %30 being 'autogynophiles'. That means that using Blanchard's own hypothesis, trans women being autogynophiles would mean they are more like cis women than less like them in that regard. If Blanchard had decided to bother using
a control group, perhaps he would have found that himself. Or if he had bothered to use samples that were not from the same clinic. Or if his results had ever been replicated. Basic scientific method issues arise from his work that would normally get any actually skeptical community to laugh his 'study' out the door as, at best, a poorly done pilot study.
Here is a brief overview of many of the problems in his work, but of course the real interesting stuff is in the studies that paper cites.
Similarly, and this might interest you specifically because you are concerned about children, studies showing very high rates of desistance among children identified as trans have been shown to be very flawed as well. Specifically, they used outdated criteria to identify trans gender children.
25% or
40% of those children simply don't meet the criteria to identify as trans gender to begin with, so of course they aren't going to be found to be trans gender at a later date. Indeed, the studies showing very high rates of desistance didn't even ask the question 'are you a boy/girl?' of the participants.
Therapists have actually shown a very high rate of identifying trans children over time. (If all the links before are too much to go through,
this article lays it out pretty well if a little over-simplified, and seems to be the most related to your interest.)
Yes, they do actually use feedback from the subject to determine that, but that does not mean it is 'just feelings'.
This quick overview from 2016 has only had more evidence in support come out after.
Notice where many of these links get published and cited. NIH, WHO, APA, Harvard...not mommy blogs. Yeah, a couple are to trans-positive pages but of course they're going to compile articles that link to evidence supporting their view.
Oh, and every time someone cites 'male pattern of criminality', know that the author herself of the work they are
misquoting disagrees heavily and specifically with them. It emphatically does NOT show that trans women are as likely as cis men to commit violence against cis women (ironically it is cis lesbians are more likely too, not that this means they should be banned from locker rooms).
Now, it isn't that this topic overall doesn't have some aspects that are genuinely confusing, or debatable, or lacking enough good data that has me so 'over' trying to explain to the general poster what is going on. How to deal with some aspects really is difficult with a lot of room for valid views. What has got me that way is how such nakedly bad 'science' and reasoning is used to bolster some pretty silly positions and being taken as valid reasoning.
Blanchard's work is of no utility to the discussion besides to show what the anti-trans gender people are desperate enough to grasp at. Gender-affirmation therapy (which is NOT just to transition tomboys to men but “listen to the child and decipher with the help of parents or caregivers what the child is communicating about both gender identity and gender expression") isn't the scientific mainstream's most supported method for no good reason; it has evidence, predictive value, and repeatability supporting it.