Disclaimer: opinion is not, and never should be, correlated to fact.
Like @Woodman I agree that gender should not be seen as a thing before puberty. Children are children, regardless of an existence or lack of any combination of genitals. That there is such a separation between boys and girls at such a young age is a symptom of a sickness within society wherein men are prepared from boyhood to do “masculine” tasks, and women are prepared from girlhood for “feminine” tasks. This is most obviously demonstrated by the “dolls are for girls, JCBs are for boys” paradigm where you are preparing the girl for maternity and the boy for graft.
Considering the equality we are still trying to instil into society, the top down approach does not work and simply prolongs the amount of time before men, women, nongender, polygender et al are seen as equal. Raising a boy through default and traditional masculine teachings, and then suddenly telling them that they have to accept that masculinity isn’t the default causes confusion, stress, and undue shaming if they feel that they are indeed not as masculine as their upbringing. The same is true for girls, obviously.
Ideally we should work from a bottom up scenario where children are still gendered, there is no inherent problem with being physically male or female or trans et al, but the gendering is not enforced by typical roles. Girls should be able to play with guns and cars and those adorable miniature Black and Decker tool kits and not be told that this is inappropriate, and if a boy wants to play with dolls then he damn well should be allowed to. Disallowing this, or shaming it, or ridiculing it, reinforces the gender difference that causes the divides in society as we see today.
Puberty though is where the child will start to inherently know who they are. It may be at the beginning, aged 8 or 9, or it may be when they’ve finished growing at 20 or 25, but when they know they know and it is not up to anyone to tell them otherwise. If they have been able to grow up in a gender neutral environment, there will be no shame, no ridicule, to their – I had to cut myself off typing choice there. That is entirely the wrong word. It’s not a choice. I, personally, am gay. I know this to be true. This is not something I chose to be, indeed the knowledge of it caused no end of misery in my teens because I had a mixture Catholic and Anglican upbringing. And I know this is sexuality not gender but in this specific case my upbringing did indeed cause problems with who I am – just like it causes problems with transexual people in adolescence. This is also why I believe this to be true; I feel almost certain that if I had been raised in an environment where there had been no stigma attached to the ideas of… sexual deviance to use a strong but accurate word, then I would have been far more comfortable and far less miserable. I imagine that the same would be true for trans people growing up in a gender neutral environment. Heck, I don’t have to imagine, because even though I came to terms with my sexuality years ago, I still feel literally guilty whenever I do something considered feminine.
Sorry, this has turned into a wall of text. TL;DR: enforced gendering in children leads to a society of fear and ostracisation. Oh hey, just like society right now!