Why do some korbanot need to be brought as male animals, and some as female animals?
Rambam explains that the animal brought, and its gender, corresponds to the greatness of the sin committed:
Guide for the Perplexed 3:46
The greater the sin which a person had committed, the lower was the species from which the sin-offering was brought. The offering for worshipping idols in ignorance was only a she-goat, whilst for other sins an ordinary person brought either a ewe-lamb or a she-goat (Lev. iv. 27-35), the females bring, as a rule, in every species, inferior to the males. There is no greater sin than idolatry, and also no inferior species than a she-goat. The offering of a king for sins committed ignorantly was a he-goat (ibid. vers. 22-26), as a mark of distinction. The high priest and the Synhedrion, who only gave a wrong decision in ignorance, but have not actually committed a sin, brought a bull for their sin-offering (ibid. ver. 3-21), or a he-goat, when the decision referred to idolatry (Num. xv. 27-26). The sins for which guilt-offerings were brought were not as bad as transgressions that required a sin-offering. The guilt-offering was therefore a ram, or a lamb, so that the species as well as the sex were superior in this latter case, for the guilt-offering was a male sheep. For the same reason we see the burnt-offering, which was entirely burnt upon the altar, was selected from the superior sex; for only male animals were admitted as burnt-offerings. (Friedlander translation)