This passage raises a lot of questions. I would like to here the thoughts of others;
as to why there needed to be a sin offering
Why she was in her impurity longer for a female child verses a male child
I love this type of questions. While we know that laws of this nature don't apply to us, God did put them in the Bible for a reason. And we are to study them.
You'll get a lot of answers here.
But ... here's mine for what it's worth.
[1] Why the sin offering for merely giving birth? Being unclean was not a sin per se, but women and men alike were declared unclean in regards to all types of bodily emissions.
Giving birth and experiencing pain was part of a woman's curse. It still is. A curse upon women because of sin. While having babies and raising children is a great blessing and joy - the initial pain and bloody mess is a curse.
In my opinion (and I am no expert), the sin offering was for having to engage in the effects of a curse from God. An appeasement, in other words, for
being cursed as a pregnant woman and giving birth in such a messy way and bloody way.
While don't women still have to do this? Same reason we don't do any of the strange ceremonial laws. The only shedding of blood that cleanses and saves is Jesus Christ's blood.
[2] Why a longer period of seclusion is a baby girl is born? Did you know that it's not uncommon at all for baby girls to be born with a bloody discharge from their own vagina and to experience one once brought home even?
Some say it's because of a hormonal exchange between the mother and the baby girl, but I don't know.
Hmmm...
TWO females having a bloody discharge. Hence, 66 days for seclusion as opposed to 33 for a male child.
There is no penalty here. No favoritism.