In a family, does the birth of a son vs daughter, signify anything with respect to Pitru-s (ancestors)?

Question

Scriptures suggest that, a person himself gets reborn as his own children, whether boy or girl.

Bhishma said, 'The son is even as one's own self, and the daughter is like unto the son. How, therefore, can another take the wealth when one lives in one's own self in the form of one's daughter? Section 45 Anushasana Parva

Having children is essential to pay the debt to ancestors (Pitru runa):
Is it not obligatory for a householder to try begetting children?

Usually female child would marry to another family lineage, while male child would continue the same family lineage.

Question: What is the terminology behind, when a Pitru is reborn as a girl or boy child?
_{e.g. Does it mean that, being a girl they want to change the family values and being a boy they want to retain the family value system?}

By this question, I want to understand:

• What could be the reasons for many families insisting for a boy child
• Why in some families, only girl children are born majorly

Answer 1

That is not the meaning of what Bhishma said. From Satapatha Brahmana:

atma vai putra-namasi

Son is called Atma.

How can Man be same as Son when there are 2 distinct jiva-atmas ?
Now, we have to dig into what the word 'Atma' means.
I can't find reference, but heard in upanyasam, it means:

That which attains what it wants

Now, we can see why Vedas say so - whatever desires a man was unable to fulfill in his life, he can fulfill through his son, like buying own house, or becoming a big business man or musician, if he educates and drives his son to accomplish those goals, he gets the same satisfaction or even better, than if he attained his own goal. We see this many times in real life, whether father really wanted to be a cricketer, but his father didn't have the means, so he gives his son all the opportunity (and also unwanted pressure sometimes).

So, the Pitrus being born again in same lineage is not the meaning of that quote.

Why only male or female children being born, is very complex karmic tangle, that can give rise to opinion based answers, one of which I'm going to give below.

Based on just personal experience, I have noticed that many orthodox brahmana families, where the father & mother performs nitya-anushtana and follow Vedic achara, they happen to beget at least one son, as though given for the sustenance/upliftment of that lineage.

Vedas themselves have a benediction for those who perform Agnihotra:

Pashyati Putram. Pashyati Poutram.

He shall see a son. He shall see a grandson. (Meaning both that he will live long, and his lineage will continue)

Scriptures also say, beget many sons, so that at least one may do Gaya Pinda-Pradhaan.

Then again, for the man who begets a daughter and gives her away at right age to a guna-vaan brahmachari, his lineage get Brahma Loka:

Kanyam Kanaka Sampannam kanakabharanairyutham
Dashtami Vishnave Thubhyam Brahmaloka Jigeeshiya

whereas if you get your son married, all you may get is Naraka in the form of Saas-Bahu ladayi :)

Any case, just because a son is born, doesn't mean Pitru Runa is satisfied, because the duties that son must fulfill are 3:

Gayayam pinda dhaanam (do gaya shraddham once a lifetime)

Pradhyabtham bhoori bhojanath (do yearly shraddham, and monthly tharpanam - even after having gone to Gaya once)

Jeevitho vakya karnaath (obey them when they're here)