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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
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
The question you ask and what you what you understand has no relation at all. Birth of a new born baby depends on the father chromosome Y. So, this is something from father's gene and depends on the time of copulation. Mothers have nothing to do with it. People who don't know it will oppose birth of female in their families. Why do families insist on boy/girl is a social matter and based on personal beliefs of the family (E.g Some want their dead father to be born again). Many insist on female child also.
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:
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