I suspect we can date the concept of the “missionary position,” if not the specific name, to the moral guides the clergy drew up during the Middle Ages. These were meant to be aids to hearing confessions. The purpose of marital sex was procreation, not pleasure. In their most developed forms, the guides prescribed how marital sex should be done: at night, partially clothed, and only in the “missionary” position with the man lying prone on top of the woman since anything else (esp. woman on top, where the semen could spill out and the woman seemed dominant) might prevent conception, lead to birth defects, or arouse too much pleasure. Other positions were, in fact, considered a form of sodomy, i.e., unnatural. Even passionate kissing and foreplay were sinful; they might distract from the procreative goal of intercourse.

Though the name itself seems connected to Kinsey's misapplication of reports from anthropologists, I suspect the position it describes dates back to this long tradition of Christian guidelines about the "correct" sexual position.

Strangely enough, I asked a similar question once. Maybe you will find the answer helpful.

I don't think the church invented sex, so I imagine the answer is, "Having sex."

I do have a follow up question though, what makes the missionary position any more acceptable than anything else?