Do dogs have gender?

I noticed that Franklin's Dogbook page has a 'gender' field. At first I thought that a bit absurd. Franklin is a boy-dog, but that is his sex, not his gender. Sex is biological, gender is an aspect of social identity. Surely Franklin can't have an identity. He doesn't think about what having the vet remove his testicles instead of ovaries means to his relationship with dogs, people, and the rest of the world.

Yet he does have an identity imposed upon him. People define dogs with all kinds of labels: he's a beagle/basset mix, he's a squirrel hunting enthusiast, and he's a boy dog. Just as parents express their child's gender identity by choosing the blue onesie or the pink onesie, Franklin had to have the manly lobster-patterned harness and not the floral one. So must gender be a self-defined category, or can this identity be determined externally?

To further complicate matters, other languages ascribe genders to inanimate objects. In Spanish, plates are male- los platos- while spoons are female- las cucharas. However, it seems the gender applies to the words, not the objects themselves. Spanish-speakers do not think of plates as exhibiting masculne qualities and spoons feminine qualities. Two words that mean the same thing can even have different genders. (A cup can be la tasa or el vaso.)

The difference between animals and tableware is that they have a definable sex, which makes gender assignment seem logical. We use gender to make sense out of the role played by sex, so to make dogs fit into the human world we give them human-like identities. Society gives humans sex-based identities as well. However, when a person's sex and gender are different we must respect that person's self-identification. Dogs cannot form identities, so our conceptions of them are entirely constructed by human society. So, dogs cannot intrinsically have gender, but we can ascribe gender to them and, given our conceptual link between gender and sex, doing so is probably inescapable.