I will summarise in a few lines what I have found in different sources:
- Top 2 of the sources for this point: Cabal, T., Brand, C. O., Clendenen, E. R., Copan, P., Moreland, J., & Powell, D, The Apologetics Study Bible: Real Questions, Straight Answers, Stronger Faith, Holman Bible Publishers, Nashville, TN, 2007, p. 169; see also W. W. Wiersbe, Be holy. "Becoming 'set apart' for God"--Cover.; "An Old Testament study--Leviticus"--Cover. (Le 12:1), Victor Books., Wheaton, Ill.,1996
There is no really a stigm on the sex. We can see that from the fact that the sacrifices a mother was to offer were the same for either a girl or a boy:
Leviticus 12:6-7 And when the days of her purifying are completed,
whether for a son or for a daughter, she shall bring to the priest at
the entrance of the tent of meeting a lamb a year old for a burnt
offering, and a pigeon or a turtledove for a sin offering, (12:7) and
he shall offer it before the LORD and make atonement for her. Then she
shall be clean from the flow of her blood. This is the law for her who
bears a child, either male or female. (ESV)
This is indicating that both genders were considered equal before God. However, one possible reason would be that the baby girl would someday be subject to uncleanness associated with female discharges and childbirth. So it takes longer if the baby is a girl, as a matter of communion of fate between the mother and the new born girl.
- Top 2 of the sources for this: Believer's Study Bible. Criswell Center for Biblical Studies. (electronic ed.) (Le 12:2). Nashville: Thomas Nelson, 1997. See also M. J. Lenz, Leviticus (2nd ed.). The People's Bible, Northwestern Pub. House., Milwaukee, Wis., 2002, p. 104
Actually I think this is valuable: the mother of a boy was ceremonially unclean for a week, at the end of which the child was circumcised.
Leviticus 12:3 And on the eighth day the flesh of his foreskin shall
be circumcised. (ESV)
The rite of circumcision of the male child incorporated the idea of cleansing, as well as the obvious meaning of inclusion in the covenant people of God. So perhaps it had something to do with the fact that new born males entered a formal relationship with God when they were circumcised on the eighth day and this will have an effect on the ritual status of the mother.
- Last but not least, in Daat Zkenim on Leviticus 12:5:1 there is this comment:
... it depends on the woman’s position during marital intercourse. If
she lies on her right side, she will give birth to a male child, i.e.
her ritual impurity will depart from her relatively quickly. This is
why the Torah provided for her to be ritually unclean for relations
with her husband for only seven days after giving birth. If she had
been lying on her left side, her ritual contamination departs more
slowly, and that is why the Torah put her out of bounds for marital
intercourse for a period of fourteen days. This is why Solomon said in
Song of Songs 2,6: שמאלו תחת ראשית וימינו תחבקני, “his left is under
my head, and his right embraces me.” The love-sick partner in this
poem indicates her desire to bear male children.
How about that?
I would rather go for number 2.