I think that original sin, as a whole, is something that exists in our bodies and the nature of humanity: man must struggle and repent for his sins because there is no person that doesn't have a natural sex drive which leads them to want to commit impure acts with people who they are not married to.
The genitals are regarded as not positive for the reason that they often are a drive in our lives to commit sins -- sex often causes people to betray one another, causes jealousy, and the sex drive at its' most basic levels can even cause incidences of rape, pedophilia, homosexuality, etc. I think people can understand why Christians are not thrilled about the sex drive.
I think the sex drive ties back to original sin in the sense that we all have it (I have not heard of people without libidos, but if it exists I do not think it is still a person without original sin -- the id, inside of all of us, also drives us to hate and be jealous and be petty).
