Why should only Sons carry the Yumnak (Surname) of their father, why can’t daughters?

Why is the Father given more rights over his offsprings? Why should only Sons carry the Yumnak (Surname) of their father, why can’t
daughters? How does the Surname of a daughter change just because she marries a person belonging to a different Surname? What is the
necessity of maintaining only the man’s ancestry; why not maintain that of women too?
This was the question that was puzzling me about this patriarchal system of society in my gender studies of sociology till recently, until I found out the scientific reasoning behind it.

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Humans have 23 pairs of Chromosomes and in
each pair one Chromosome comes from the father and the other comes from the mother. So in all we have 46 Chromosomes in every cell, of
which 23 come from the mother and 23 from the
father.Of these 23 pairs, there is one pair called
the Sex Chromosomes which decide the gender of
the person. During conception, if the resultant
cell has XX sex chromosomes then the child will
be a girl and if it is XY then the child will be a
boy. X chromosome decides the female attributes
of a person and Y Chromosome decides the male
attributes of a person.When the initial embryonic
cell has XY chromosome, the female attributes
get suppressed by the genes in the Y
Chromosome and the embryo develops into a
male child. Since only men have Y
Chromosomes, son always gets his Y
Chromosome from his father and the X
Chromosome from his mother. On the other hand
daughters always get their X Chromosomes, one
each from both father and mother.So the Y
Chromosome is always preserved throughout a
male lineage (Father – Son – Grandson etc)
because a Son always gets it from his father,
while the X Chromosome is not preserved in the
female lineage (Mother, Daughter, Grand
Daughter etc) because it comes from both father
and mother.A mother will pass either her
mother’s X Chromosome to her Children or her
father’s X Chromosome to her children or a
combination of both because of both her X
Chromosomes getting mixed (called as
Crossover). On the other hand, a Son always gets
his father’s Y Chromosome and that too almost
intact without any changes because there is no
corresponding another Y chromosome in his cells
to do any mixing as his combination is XY, while
that of females is XX which hence allows for
mixing as both are X Chromosomes.

Y Chromosome is the only
Chromosome which gets passed down only
between the men in a lineage. Women never get
this Y Chromosome in their body. And hence Y
Chromosome plays a crucial role in modern
genetics in identifying the Genealogy i.e male
ancestry of a person. And the Salai(gotra) system was
designed to track down the root Y Chromosome
of a person quite easily. If a person belongs to
Kumar( surname) then it means that his Y Chromosome
came all the way down over thousands of years
of timespan from the Kumar (surname) ancient forefather. This also makes it clear why females are said to belong to
the Salai (Gotra) of their husbands after marriage. That
is because women do not carry Y Chromosome,
and their Sons will carry the Y Chromosome of the Father and hence the Salai (Surname/Gotra) of a woman is
said to be that of her husband after marriage.
Pretty neat isn’t it?