I think most of the time when they claim it is unnatural, they are talking about how it is not normally accepted behavior, not because it is not found in nature. Just like eating poop or something like that. I can say it is unnatural, but I don't mean I can't find it in nature (because I can) but because I find it abnormal behavior. But I am sure some people use the term unnatural in the way you describe it.
Aslo, your point about how homosexuality is abundant in nature doesn't mean much. All species are different than each other (duh!!) each one has its own way of surviving, reproducing, and preserving themselves. It is quite possible that some species require some form of homosexuality to continue, but who knows for certain.
That still doesn't mean that the same rules for animals also apply for humans. I can't find a reason how having homosexual relations would benefit the human race. Humans depend on reproduction in order to survive, human homosexuals by default can't reproduce (I am not talking about adoption and other methods).
And some of the examples they use in the article doesn't really qualify as homosexual behavior, and it can be compared to some frats and sororities.
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