There's an enormous amount of diversity in the animal kingdom. There are great behavioral differences even between us and the other apes. Therefore, it's absurd when someone tells me about human mating behavior because of a study about North American gray tree frogs (that is an actual thing that happened). You can't just point to an animal doing something and declare what they do "natural" in some universal way. This approach is obviously set up for nothing but cherry picking, where one person picks and animal who's behavior matches their position, and then the other person picks an animal that contradicts it. Back and forth, accomplishing nothing.
Furthermore, there's a question of when it is necessary. I'm often amused at people bypassing observed behavior in actual humans to try explaining by way of the behavior of some far removed animal. It actually transpires (has on this forum, in fact) that people will sometimes disregard the direct data on what humans are actually doing to argue that they somehow should be doing something else because some fucking shrew does it or something.
Now, some attempts have been done to study broad trends in animals in the hopes of finding sexual characteristics that apply to human beings. That's a lot better, but it's not perfect. I repeat that the animal kingdom is vast and diverse, such that even an apparently broad trend across some subject animals may really be too small. It's process that remains under a fairly balanced amount of controversy even among the top scholars in the relevant fields.
I guess the thing I'd really need to emphasize is the difference between an inherited trait (a trait that is the product of genes possessed by an organism at conception) and acquired traits (traits obtained through interaction within the environment, especially after birth). Not all animals are equal in terms of much they acquire traits. Some do it very little, some do a lot, and what's extremely important is that as far as we know at this time, no animal acquires traits more than humans. This would suggest that humans are the least subject to broad rules about genetically inherited behavior.
On that note, sex and gender are different things. Sex, perhaps we can discuss, but gender, I'm convinced is so socially constructed (acquired, therefore) that there's little to be understood about human gender by looking at other animals. The only thing that strikes me as interesting there is if we find what appears to be socially constructed gender in another species (which we may have). There might actually be something to learn from that.