Ya gotta remember that side by side with all the serious stuff that was a part of ancient life, there were a LOT of 25 year olds running around strutting their stuff - especially the Greeks - and blowing off steam, since most of the population was dead by their late 30's. Our early ancestors were "just kids" for the majority of their lives. Once you get to serious city states the rules changed of course, too many grown-ups, but until you get there, it was all clans, tribes, and families with shared histories and culture, with all that implies and ancient Greece was even more so. Not always so pretty maybe, but ... human.
Where does this weird idea come from? I am afraid, but you are utterly mistaken. The ancient Greeks and Romans at least had about the same average life span we had 150 years ago, or so.
You are confusing the statistical measure life expectancy with the real life span. This man here is responsible for that type of confusion many people do have about it:
Ignaz Semmelweis, one of the unknown heroes of science and mankind and unsung life saver of literally billions of people.
Before Semmelweis happened,
postpartum infections where a common thing because the hygiene of birth giving was not there. Babies where infected always with bacteria and viruses, and it was common that 30% of the newborns died within a few days/weeks after being born.
Semmelweis introduced as simple method that the midwifes and physicians washed their hands before starting to work every time and also cleaned their tools, which reduced the mortality rate almost to 0%. This has been since then a global standard procedure.
So coming back to ancient Greek this means that if a mother gave birth to let's say three children, you can expect at least one of it to die soon after birth. The other two however were living their normal lifes.
So simple calculation: (0 years + 60 years + 70 years) / 3 = 43 years of life expectancy, roughly. Here's a controlled study below, which found out that the median age 100 BC of their Roman sample was 72 years.
So in reality ancient Romans and Greeks used to get as old as modern people get today, the only difference is just that many of their brothers and sisters died shortly after birth. Which is an uncommon thing now in industrial countries, but you can still witness e.g. in many countries of Africa.
The same applies by the way to all epochs that came after the ancient world, like medieval times.
You are right though about that most people in ancient times tried to get children soon at young age, but for a different reason: not because people died so soon, but because children were the social network of that time. And since it was common knowledge that not every birth will make it back then, they knew that needed to have several attempts for some children to come through.