If you trace a genealogy* of the term "homosexual," you'll discover that the terminology and the concept as a noun rather than a verb only came into existence in the late nineteenth century. Which isn't to say that same-sex sexual activity didn't meet with varying degrees of disapproval and social stigma prior to this time. The point is just that engaging in same-sex encounters was not thought to say anything about a person, to determine their character or nature in any way, to influence their propensities and tastes and political views and talents and personality and social status and career choice in any way. Because in this worldview, sexual activity was just that - one activity among many others - rather than a defining characteristic that made you into one of "those" kinds of people.
In The History of Sexuality, Foucault notes that in ancient Greece and Rome, people were not divided up by whom they were sexually attracted to/active with, leaving them free to love beautiful people, regardless of which type of body they inhabited. This view of Foucault's seems a bit overly idealized, given the fact that the sexuality of women and slaves wasn't even factored in, and for men there was a great deal of policing in terms of whether one preferred to be the active (penetrating) or passive (penetrated) partner. And in fact, preferring to be the passive partner was thought to indicate some degree of moral degradation and lack of character on the part of mature males, but not anywhere near the kind of defining characteristic sexual preference is thought to be in our culture. And of course, Foucault's point remains that the gender of the bodies you were attracted to was thought to be utterly irrelevant to any other facts about you.
Contrast this worldview with our current view that homosexuality is a state of being, an identity that one inhabits, a lifestyle that one lives, etc. And when you start to think about it this way, it seems really odd. Out of all the activities we engage in every day, why is this particular activity supposed to generate so much of your character and personality? Out of all the preferences and physical and psychological features of a person, why is this one thought to be so central and so influential on one's nature? And once you become aware of the sort of randomness of this method of dividing up the population, and the historical contingency of the category, it becomes pretty clear that homosexuality, as an identity and a character type, is a social construction. That's not to say that people aren't born with varying sexual preferences, or that homosexual people as a social and political group don't exist. The point is that without this particular social construction and the biological essentialism and political oppression and social stigma that accompanies it, "homosexual," as a distinct type of person and a distinct class with their own political and social concerns, would not exist. It's a social construct.
Sometimes it's helpful to state it like this. There are two possible ways we could approach the issue of homosexuality in our culture. The most common liberal approach is to try to debunk the stereotypes of homosexuals and ensure their equal treatment. So the claim here is
not all homosexuals have characteristics x, y, and z, and it's discriminatory to believe that and treat them differently on the basis of this belief.In contrast, the social constructionist says
there are no homosexuals, only people who have all different kinds of sexual preferences, and these same people all have their own unique combination of propensities, characteristics, talents, political views, social tendencies, etc.See the difference? The second view automatically leads to equal treatment, because it insists that we're all just people, and our sexual preferences are not relevant to anything other than our own relationships.
From this view it's indeed very odd to refer to animals as being gay or lesbian or bisexual. As creatures who are not embedded in a cultural framework like we are, they technically cannot be gay or lesbian or bisexual. They can engage in same-sex mating and pair-bonding. But they can't be gay. On the other hand, if we were thinking clearly about this, neither could humans.
* In the Foucauldian (Nietzschean) sense of investigating a concept or cultural attitude in order to show "that a given system of thought [...] [is] the result of contingent turns of history, not the outcome of rationally inevitable trends."