But why? Why can't everyone just live and let live?
We could. And that would be the logical goal of a civil rights movement.
But this is not a civil rights movement. "Trans" people are not being excluded from society in any way, like gay people, or women were. They already have as many rights as anyone else.
But there are a group of activists (not representing all "trans" people) demanding special treatment, at the expense of others.
A relevant piece by Jane Clare Jones:
Gay Rights and Trans Rights - A Compare and Contrast
What I want to do here is think through why the concept of ‘discrimination-as-phobia’ worked for the gay rights movement, and why, despite superficial similarities, it doesn’t accurately capture what is at stake in the trans rights debate, and actually serves as a tool of political propaganda and obfuscation to push that agenda through. That is, I’m going to argue that accusations of ‘homophobia’ were a politically powerful and basically on-the-money part of gay rights discourse, while the use of ‘transphobia’ is an inaccurate parallel which grossly distorts public perceptions of the issues involved in the trans rights debate, and is doing so in the service of actually preventing that debate taking place.
[...]
The key thing to understand about trans rights activism is that, unlike gay rights activism, it is not just a movement seeking to ensure that trans people are not discriminated against. It is, rather, a movement committed to a fundamental reconceptualization of the very idea of what makes someone a man or a woman. In theory, this equally affects both men and women, but in practice, almost all the social pressure is coming from trans women towards the idea of ‘woman’ and the rights of women. And that’s because, when it comes down to it, this whole thing is being driven by male people who want something female people have, and that something, is, in fact, our very existence.