Yes, puberty is horrible for everyone. But imagine adding transgenderism to the mix. Along with everything else, your body gradually turns into something that at best you feel no connection to and at worst actively horrifies you. (There are different kinds of transgender people.) The point of trying to catch it at puberty is to reduce the self-rejection (dysphoria) over a lifetime. Because, while your sex can't be changed (non-trans people always think trans folks don't know that,) neither can your gender be changed. And it turns out - and it's been tried both ways - that it's more successful when you change the appearance of your body to suit your mind than it is to change what you experience in your brain to suit your body's genital configuration.