Its really just the difference between biology and what society has shaped us into.
We used to have was shorter lives so the younger we could start having children the better. Remember, at some point in our evolutionary history, sex and having children was purely for the survival of our species. We can only have one child at a time (unlike cats, pigs, dogs) so the younger we could start having children the better for our species.
The only reason this biological process is looked down upon at such a young age is because of the extremely complex society we have. You are expected to be old enough to have an education, get a well paying job, specialization education in a specific field, experience in life, a house, and the personal and emotional stability that is needed to take care of a child before even considering having a child because you have to take care of that child for a good 16-20 years, and there is still work to be done after they move out.
Think about it, most animals raise their young briefly and send them out into the world, most new born animals can walk as soon as they are born, but society evolved with us, and there is a lot societal pressure to be responsible enough to have a child.