The people saying that gender roles and stereotypes are the only reason people are trans are incredibly ignorant. Trans people do not transition because 'they enjoy things that are traditionally enjoyed by people of a different gender'.
If you are a female, then you are a female, someone telling you that you are a male doesn't make you male, having a vagina also doesn't inherently make you female. In the same way that being in a relationship with a woman as a bisexual woman doesn't make you a lesbian.
The 'trend' is not a trend, it's a change in societal understanding of trans people, and the age that people figure out their gender identity. It's also a reduction in trans young people dying by suicide, as well as an attempt to reduce violence towards trans men and women.
Gender identity, much like sexuality, is innate and can be very varied (kinda like the kinsey scale or similar) so no, not all people are women, or men. Some people are both, some are neither, some change depending on when you ask.
Is it wrong to allow children to transition? Yes and No. Children should be allowed to explore their gender identities, and should be encouraged to be open and honest about their feelings, but also to know they can change their minds. I don't think surgery should be offered to the under 18 age group, because it's permanent. But hormones can be reversed if needs be, and puberty can be 'postponed' which allows the young person more time to figure things out. We wouldn't dream of telling a child they are 'too young' to know their sexuality?
As for the OP, no I don't think that's wrong and YABVU. Language is important and it's incredibly arrogant to assume you know everyone's gender identity, and it's not difficult or offensive to use gender-neutral language. Otherwise you're assuming you can guess someone's gender from their appearance which is pretty rude.