Jenner says transgender girls in women’s sports is ‘unfair’ Rational points. However, you wrote "I don't think it's a thing that people are faking being trans or gay to be cool." Not faking. Confused, awkward, immature, and then becoming 'trans' gives them an identity, purpose, cause, & support.
You wrote "In fact many children outgrow this at puberty." You softly pointed out a significant issue which the trans community seems to bury.
KQED: "The phenomenon of transgender children "growing out of" their transgender identity by the time they are adolescents or adults is called “desistance” by gender researchers.
"For decades, follow-up studies of transgender kids have shown that a substantial majority --
anywhere from 65 to 94 percent -- eventually ceased to identify as transgender. ...
"In Amsterdam, clinicians at the Center of Expertise on Gender Dysphoria are much more cautious about recommending social transitions because of the statistics on desistance."
https://www.kqed.org/futureofyou/441784/the-controversial-research-on-desistance-in-transgender-youth
For the record, I know a group that is primarily lesbian women. The most level headed person there is a trans man. Really a nice man. But even his lesbian partner admits that "Fred", in his 40s, was indecisive about the transition. Has a career, educated, in a LTR, and confused.