Our Gemara discusses the requirement that an olah sacrifice must be a male animal and a sin offering must be a female animal. What is the reason for this?
Rambam in his Guide for the Perplexed (III:46) offers practical reason: The greater the sin, the less dignified and worthy is the sacrifice. The male animal is more valuable (it can be used for burdens in the field and can sire offspring. Therefore the male animal is set aside for the Olah, which is for light offenses, and is a full offering to G-d with no human consumption. The sin-offering is for a major sin, and is of lesser esteem in terms of the actual value of the sacrifice. Similarly the Minchas Chattas, contains no oil or frankincense.
While there is a logical progression here, Maimonides’ explanation seems counterintuitive, as it would seem a more serious sin would require greater financial commitment.
Rabbenu Bechaye (Vayikra 1:9) offers a mystical interpretation, which I will try to explain. In the mystical theology, sacrifices are an effort to unify the various discordant and non-unified “powers” of Hashem that manifest in this world. There is a basic kabbalistic concept that Hashem needs “our help” in the material world to manifest His power. That is why many rituals involve symbolic acts down here, which activate powers up there. For example, in the Bais HaMikdash we light the Menorah to bring light to this world, and we bake the showbread to bring sustenance. There also is a requirement to have an earthly fire meet the heavenly fire on the altar, another illustration of this dynamic.
In the mystical World, maleness is symbolic of action and doing, while femaleness represents receiving. This is represented in many archetypal facets of men and women. A man “makes“ a woman pregnant, and she receives the seed. Men tend to be more aggressive and action-oriented, while women tend to adapt and adopt more to their surroundings, as opposed to changing the surroundings. This is not to say anything about how a man or a woman can or should be, rather these are symbolic mystical representations about matters that are instinctive on a broad level. Understanding the symbolism, the Olah sacrifice is brought completely to G-d, and all of its physical elements are burned and ascend to heaven, having the matter coming very close to the primordial state of G-d’s undiluted will and potential. It is also notable that the Olah Sacrifice is for sinful thoughts as opposed to misdeeds, that is not so much for trespasses as for lack of action. That is why the sacrifice taps into the male mystical archetype, in order to inject more action and restore more action to the G-dly powers in this world.
On the other hand, the chattas sin-offering is from a female animal. A sin is a trespass and represents an overactivity and over aggressiveness. Therefore, the more passive elements of the female archetype needs to be restored back to the powers of God in this world.
As I have commented in other discussions similar to this, the connection between psychology and mysticism is often a matter of using different words to express underlying similar concepts and truths. Within ourselves, we sometimes have a lack of aggressiveness which needs to be restored, and sometimes we have too much aggressiveness which needs to balance out with passiveness. The enactment of the sacrifices can be understood as stimulating a mystical and unconscious process of restoration.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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