The human sexes are actually genetically separate species. The genes are even compartmentalized. They struggle for dominance despite being dependent on each other.
The male wants his offspring (be it either male or female) to get the maximum possible amount of nutrients from the mother. This even to her detriment. The mother, on the other hand wishes to pass on her genes, but , of course, wants to live to produce more offspring. This tug-of-war has led to what is termed genetic imprinting. That is to say, paternally supplied genes promote growth while maternal ones tend to reduce it.
For example, in the placenta, the fathers allele for the Insulin Growth Factor 2 is expressed while the *receptor* for Igf2 is controlled by the allele of the mother.
Our genes are compatible for the sake of reproduction, but, even on the cellular level, we are at odds with our final objectives. To say our genes are compatible is not really saying much. Most of the genes for all mammals are compatible. It is only in small ways they differ, making producing offspring unlikely or impossible. Thus, men and women can be thought of as different as humans and cats. The truth is we would probably never really get together at all were it not for sex. We have a mutual need, but not for the same reasons; not really. And that need can be satisfied by other means, and for some, even by other species.