So there are two different way to look at this: first, how does it happen, and second, why does it happen.
In humans (and many species) it happens due to sex chromosomes. A cell has two copies of each chromosome, and for sex chromosomes in people women have XX and men have XY. Each egg or sperm gets _one_, in women that’s an X or an X, in men that’s an X or a Y. There are equal numbers of X and Y sperm produced because each sperm cell originally comes from an original cell that has both X and Y and divides to produce sperm. They get made in sets of four, two with X and two with Y. The X’s produce females, the Y’s males, providing a 50-50 ratio. The ratio at birth is a bit different (because male embryos are more likely to die) but it’s pretty close.
Now, not all animals do things that way, but nearly all have a 50-50 ratio, and for good reason. Imagine a situation where, for whatever reason, the ratio is imbalanced…a species naturally has a surplus of one sex. Any parent producing the usual ratio where most offspring are the dominant sex will have offspring which have a hard time finding a mate. But if any parent happens to have some genetic setup which allows them to produce more of the _rare_ sex, all their offspring will have an easy time finding mates and will therefore reproduce a lot…and will transmit that “have more of the rare sex” trait widely. It’s called balancing selection…basically, any individual with a tendency to produce more offspring of the rarer sex will leave more descendants. Over time this results in a balanced sex ratio.
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