We've all heard about the gay penguins, and then all the other news about how all manner of other animals knowingly partake in non-procreative mating and pair bonding with members of their own sex. Now there's more and more news about transsexual animals. There's a myriad of ways in which animals reproduce - most people already know about hermaphroditic worms and such. There are hundreds of fish species that are successive hermaphrodites: they start out as one sex and change to another (and sometimes go back and forth a few times a day). But that's just part of those animals' typical lifecycles. Now there's more attention being paid to species where only a few individuals of the population change sex. Today in Wired there was this article about a bellbird in New Zealand that started off female but now looks and acts male. Some other birds have also been observed to make this change. I don't doubt that with more observation we'd see this phenomenon in even more species. It's probably just more apparent in birds because of the marked physical and behavioral dimorphism in many bird species.
Well, we can't know what exactly is going on in the animals' minds; the closest we can tell is from their behavior. But it shows that starting as one sex and ending up as another, even among 'higher' animals, is not strictly a human weirdness.