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Woman is the biological default. That's why women have redundancy on the 23rd chromosomal pair, whereas men have a special "Y" chromosome - leading to much higher rates of genetic disorders in men. That's why in infant male humans, the testicles have to descend. And so on. Both from an encoding and from a developmental point of view, a man is a woman altered to be masculine. And testosterone is what does that altering.
Yes, it could have been different. We can imagine a species with a neutral default, which then gets altered to be either masculine or feminine by different sex-encoding hormones. But that's not how humans came about.
We don't have to imagine. We can look at birds, where the sex chromosomes are the opposite. I haven't looked at them, so I don't know how much is a consequence of the chromosomal structure. But, for some reason, I'm skeptical that most people who pontificate their role have looked either. The points about hormones and development are more reasonable.