The sutta quote below explains the duties of lay children to their parents and parents to their children. It's based on the cultural norms of Indian society in 500 BCE.
Children should maintain the kulavamsa, which can be translated as "family traditions" and also as "family lineage" based on the PTS Pali-English dictionary entries on kula-vansa and vansa.
Parents should "connect their children with a suitable partner", implying arranged marriage, which again, is a common practice 2500 years ago in India.
A child should serve their parents as the eastern quarter in five
ways, thinking: ‘I will support those who supported me. I’ll do my
duty for them. I’ll maintain the family traditions. I’ll take care of
the inheritance. When they have passed away, I’ll make an offering on
their behalf.’
Parents served by the children in these five ways show compassion to
them in five ways. They keep them from doing bad. They support them in
doing good. They train them in a profession. They connect them with a
suitable partner. They transfer the inheritance in due time. Parents
served by their children in these five ways show compassion to them in
these five ways. And that’s how the eastern quarter is covered, kept
safe and free of peril.
Sigalovada Sutta or Singala Sutta (DN 31)
The same thing here:
“Bhikkhus, considering five prospects, mother and father wish for a
son to be born in their family. What five? (1) ‘Having been supported
by us, he will support us. (2) Or he will do work for us. (3) Our
family lineage will be extended. (4) He will manage the inheritance,
(5) or else, when we have passed on, he will give an offering on our
behalf.’ Considering these five prospects, mother and father wish for
a son to be born in their family.”
AN 5.39
This is of course not mandatory, as adults could also choose to become monks and anagarikas who obviously don't usually marry or have children. Anyone who marries and has children before becoming monks, would have to abandon their families in pursuit of the monastic life.
Also, it's important to note that one could become a monk or nun, only with the explicit permission of all their living parents. If your parents forbid you from becoming a monk, then you will never be allowed to join the monastic order.
For those interested in monasticism:
'I have sons, I have wealth' —
the fool torments himself.
When even he himself
doesn't belong to himself,
how then sons?
How wealth?
Dhp 62
Either way, one shouldn't waste their youth and should use it fruitfully. But the verse below talks about gaining wealth and not about getting married and having a family.
Neither living the chaste life
nor gaining wealth in their youth,
they waste away like old herons
in a dried-up lake
depleted of fish.
Neither living the chaste life
nor gaining wealth in their youth,
they lie around,
misfired from the bow,
sighing over old times.
Dhp 155 - 156
"Chaste life" above means holy life or monastic life.
