That’s actually a modern invention. Originally, 他 (they, sg.) was the only one used, but then someone added 她 for the literal sole purpose of translating western European works – as in many of those languages there, it’s all gendered.

Try to translate this for example: “He wants a cookie, and she wants a mango.”

If translated literally-ish, you’d write: 他有饼干和他有芒果, which yields “They want a cookie, and they want a mango”. It’s ambiguous.

So if one really wanted that, why (in my view) not do it as: “他有饼干和那女的有芒果”? That meaning, “They want a cookie, and that gal wants a mango.”