That "constant state of flux" is what makes your body into a prison that you have to inhabit the rest of your life. Every single trans person I've met desperately wishes that they had transitioned earlier. I transitioned relatively early, and I'm still intensely jealous of trans teens who are getting proper treatment today. My older friends who've transitioned in their late 20s-40s regard their lives as being hopelessly ruined. And some of them repressed their trans feeling for a while, only to have them come back later with vengeance. But you never hear about those people in these arguments.
My mom said something similar about "curiosity" to try and convince me that I couldn't be trans. As it turns out, what she meant was "when I was your age, I wanted to cut my hair short." Likewise, pretty much every story I've heard like this turns out to be either obvious lies meant to discredit trans people, or something that would have been easily sorted out by a psychologist. Eg. I've heard of gay people wishing they were another gender so that they wouldn't get bullied for their orientation. No decent professional would mistake that for genuine dysphoria.
But even supposing that your psychologist was incompetent, you still would have socially transitioned in some capacity before you ever started hormones. This almost certainly would have let you know if transitioning was really right for you. And even if it didn't, and you went all the way to starting estrogen, you could always stop if you didn't like what it was doing. Estrogen works very slowly. I've been on it for three years, and I know cis men whose boobs are bigger than mine. If I changed my mind, I could easily start living as a man again.
It's absolutely unfair to impose life-ruining misery on trans teens because of the off-chance that it might do a fraction of the same harm to a cis person.