What law prohibits family members from intercourse with each other?

Answer 1

All States have laws against incest and against marrying someone closer than a 2nd cousin (i.e. father, mother, sibling, or first cousin).

Laws against intercourse with a close family member were enacted to avoid increased risks of genetic conditions, which can cause higher miscarriage rates, stillborns, or lifelong deformities, etc. Facial-cranial (face, skull and brain) and spinal deformities can cause shortened lifespan or lifelong disability. As a species, humans must choose from a wide gene pool in order for the species to survive AND thrive.

Also, social and religious customs have long recognized that intercourse between family members can disrupt families and communities. Possibily because people have witnessed the negative outcomes from sex with a close family member, religious and the community react with disgust and anger toward anyone who breaks the social norm laws.