Marriage in the United States shall consist only of the union of a man and a woman. Neither this Constitution, nor the constitution of any State, shall be construed to require that marriage or the legal incidents thereof be conferred upon any union other than the union of a man and a woman. (CNN)
Biologically, there are males (XY), females (XX) , and other (XXY, XXX, XYY, etc., sometimes called intersex), but the terms "man" and "woman" are social constructions. If we tried to define marriage by the genes, then up to 1% of the population  would be entirely unable to marry because they don't fit the combined biological definition and social construct of "man = XY" and "woman = XX".
I guess we could instead define it by birth certificate, which actually is the least of many evils, since you can get your birth certificate gender changed after a sex change operation (so a MtF transexual can marry a man ), but you don't have to (so a MtF can also marry a woman ).
Ah, the amusements of loopholes. Bring on the lawsuits!