What is the non-biblical argument against homosexuality?
It is easy to show Scripture condemns homosexuality. Can a case be made without referring to Scripture?
One way is by showing how homosexuality violates natural law. Many people have a basic ethical intuition that certain behaviors are wrong because they are "unnatural." For example, virtually everyone would agree that bestiality (sex with animals) is unnatural. We perceive intuitively that the natural sex partner of a human is another human, not some lower animal. If one can argue in this fashion, then one can also argue (drawing on the same intuition) that the natural sex partner of a man is a woman and of a woman, a man.
This is also supported by considering the nature of reproductive organs. It is clear that in nature some things have inherent functions (called teleologies by philosophers). In the human body the function of the heart is to pump blood, of the teeth to tear and grind substances (usually food). Reproductive organs also have teleologies which can be easily discerned. The physical design of each organ, as well as the process of human reproduction, is geared for this function. To violate this arrangement is to engage in an unnatural act--thereby offending God, the author of natural law.