Unnatural sexual behavior
In most cases, in fact, it's not true. Animal sexual behavior is very varied, and unsurprisingly, it's our fellow mammals who tend to be the most imaginative. Masturbation, promiscuity (in both genders), oral sex, foreplay, incest, rape, homosexuality (in both genders), erotic dances to whip up a partner's interest, sexual play among adolescents, and even lifelong commitment to a single partner -- all these things have been observed among other mammal species and are common enough in at least some to qualify as normal behavior for them. (Note too that a couple of these examples remind us that blindly taking what occurs in nature as a guideline for what should be acceptable among humans would be rather dangerous.)
But there is one form of human sex-related behavior (indeed, one which the moralists consider an essential prerequisite to sex of any kind) which has no counterpart in nature. It's marriage.
No naturalist studying any species on Earth has ever reported a case in which two animals who wanted to mate with each other insisted on finding a third animal to stand around reciting mumbo-jumbo at them first. Only humans do that.
Personally I've always found the concept somewhat insulting. Its underlying assumption seems to be that the feelings a man and woman have for each other are not enough in themselves, and need to be "legitimized" in some way by bringing a third party -- the church, the government -- into the relationship to provide its stamp of approval.
In fact, if people feel motivated to be monogamous, they will be, with or without a piece of paper from the state. And if they don't feel motivated, the piece of paper probably won't help.
Others are entitled to their own views, of course. But denunciations of behavior as "unnatural" are impossible to take seriously.