Missionaries are all 18-21-ish, and they get trained for like a month. There's no way that's an official answer in any way, they're just repeating whatever some other missionary told them. I guess it kinda makes sense with the "multiply and replenish the earth" line from Genesis 1:28, but that's probably as far as the thought process goes.

And yeah, the actual origins are probably somewhere between the more official "take care of women" line and "wanted to bang women" line. But the fact remains that many men didn't bang all of their wives (or so they claim), so it's probably a mix of both.