I think that this is a notion carried forward from the past, from a time prior to the development in detail of the explanatory theory of evolution. It was one of those religious explanations that, like all of them, ends with the intellectual cul-de-sac that it is one of 'god's mysteries' that will be explained in due time. It once provided the 'answer' to a human question that empirical observation, logic and science had not then figured out.
'God's mysteries' was an explanation before the time there was significant biological study of simplistic life forms (genetically and otherwise) that are asexual and reproduce without partnering with another of the same species. Before it was observed (and explained) that higher, more complicated organisms' sexual reproduction evolved to make the offspring stronger by splicing two sets of genes together (avoiding the frailties of 'inbreeding'). Before it was realized that gender differentiation and the need of higher organisms to sexually interact to reproduce was part of the evolutionary process. (by the way, I for one find that life is much more enjoyable because of the sexual desires and relations

In light of the scientific explanation, the religious one has become an archaic absurdity.
The Mormonism version of the god's mysteries for gender assignment has included that this assignment is an eternal assignment. If you are male in this mortal existence, then you will be male for eternity in the CK, for example. Jehovah and Lucifer were 'sons' (gender-specific offspring) of Elohim (and unnamed mother(s) in heaven) in the pre-existence, before Jehovah got a physical body (and Lucifer still has not). So this assignment even predates conception and birth into mortality, these assignments pertained in the spiritual pre-existence. These gender assignments have, per Mormonism, some eternal consequence, extending in time both pre- and post-mortality.
So if animals are of relatively little spiritual consequence that we may use them for human purposes, including killing and eating animals for human pleasure (human life can be sustained by being a vegetarian--cf. LDS Mormonism having set up and maintaining a for-pay hunting preserve), why are animals given these same/specific/significant spiritual assignments of gender, male and female, in the Mormon scheme of things? If so incidental to humans, why would animals be imbued with these sacred assignments of gender?
The female gender of many, but not all, species is the more nurturing. This depends in part on the practicalities of life faced by that species. After conception, the males of some specifies play a significant role in the gestation. For example, after the emperor penguin female lays the egg, the male takes over caring for the egg until the chick has developed to the point that it emerges from egg shell. In the human species, the female handles the gestation (often absent the male) and is the primary nurturer for the child in the early years of development after live birth.
If god thought only one human gender was worthy to entrust with his power (priesthood), why would it not be the more nurturing-inclined of the two genders? Isn't nurturing of us, god's children, a quality that is ascribed to god? Does that suggest that the real gender of god may be, as my friend zeezrom is inclined to hope, female?
Is the fact that some religions (e.g., LDS Mormonism) are hanging on to the old, archaic and sexist notion that the male gender has some religious significance that god would only entrust his power to males evidence that such religions are outmoded and marginalizing themselves over time, as mankind learns more about its circumstances and is able to better explain them?
It took LDS Mormonism until 1978 to realize it was outmoded and marginalizing itself with respect to the denial of the priesthood to blacks, even though the United States had passed the 14th Amendment on July 9, 1868, giving legal voice to the notion that governments should not be racist. The LDS Mormons tenaciously argued for another 109 years, 11 months, until 1978, that god was behind the LDS Mormons' racism and some LDS Mormons even today yet argue god was, for some inexplicable reason or only yet indefensible racist reasons, before 1978, rather than acknowledge the obvious that the LDS Mormon leaders were just claiming it was 'god' when those leaders were claiming as theological doctrine the mere notions of them as men.
The equal rights amendment did not pass, but gender equality under the law has nonetheless become quite pervasive. How many years will the LDS Mormons continue to claim that their god doesn't trust women to be authorized to exercise god's power? How outmoded and archaic will the LDS Mormons have to become before their god realizes the advanced morality of humans?
ETA: Cleaning up grammatical, syntactical and spelling errors.