While I have trouble swallowing this (I guess, following this, that Gfted1 must be horribly scarred from the experience, for one), I'm going to let it slide, and pose a question instead.
Is this an impossibility in the same sense as "a human cannot survive in a vacuum", or just a result of how our children are reared and other cultural influences? During the Classical period, girls were bethrothed just after reaching sexual maturity, generally to older men. They were mature enough for maternity. There were many factors contributing to the collapse of the Roman Empire, but women marrying and becoming mothers while in their teens wasn't one of them.
Does this even have any semblance of scientific rigour?
There are quite a few factors that go into a 13-year old not being emotionally developed enough to handle a sexual relationship, particularly with a 44-year old man, but I will address the cultural issues in comparing Ancient Rome to our modern day. In the past, that was a woman's sole purpose according to society, get married, rear children, rinse, repeat. Today's women, at least in most developed nations, are expected to get an education and to develop as an individual. When an older person gets into a sexual relationship with a younger person, they are creating a very serious reliance and it is a relationship that can easily be manipulated by the older party. The laws are written to protect young people from being manipulated and giving them a chance to get an education and develop as an individual.
There is a pretty clear difference between a sexual relationship for a boy and a girl. It can still be an emotionally scarring experience for a boy, but girls also struggle with the concepts of pregnancy. I've seen a lot of teenage pregnancies during my time as a teacher, and it is always tragic. No matter what route they go, their life is changed permanently and their childhood is over.