Do our body's require sex, on a biological level?

Yes. Basic evolution: In a village far, far away, and a long time ago, some humans wanted sex. Some humans didn't want sex. As the years went by, the humans who wanted sex got pregnant more often, had more children, and became the great majority of our population. The humans who didn't want sex didn't have many children, so those carrying the "don't want sex" trait became a smaller and smaller part of the population.