Answer: The issue centers around an act that was part of the original creation: childbearing is an act ordained and blessed by God, but Israel is instructed that the performance of bringing a child into the world brings a condition on the woman that separates her from God.
First, it is not the birth that causes the problem, but the flow of blood connected with it in the context of ceremonial law (as opposed to civil or moral law). The Bible teaches that "life is in the blood" (Genesis 9:4). Leviticus 12:6-7 shows that after her days of ceremonial waiting, the woman was to bring a sacrifice for a sin offering to be offered “before the LORD to make atonement for her; and she shall be cleansed from the flow of her blood.” The man does not give the offering—even for the child. The woman has the ceremonial problem and must ceremonially take care of it herself by faith in the payment of the blood sacrifice. Blood for blood.
One point of the ceremony is to show that defilement can be intentional or unintentional; but, it should not prevent them from doing what was commanded (to have children) or think of the act as sinful, ungodly. They must carry out what God has commanded and not ignore the incidental defilement. Sure, they can avoid it, but in so doing God’s command will not be obeyed and there will be no securing the blessing of children.
Another point of the ceremony is that God does not leave the unclean person without a way to be clean, even ceremonially. The obedient person will do what God has commanded fully, which includes trusting Him to justify the unclean person once justice has been served and payment has been rendered; hence, the sacrifices.
Ceremonies like these serve as a reminder that living in the flesh is living in a fallen world and there is nothing we can do to save ourselves, much less, clean ourselves up (even ceremonially). God must do the cleansing when we go to Him by faith in the finished work of His sacrifice that He made for us in the death, burial and resurrection of the Lord Jesus Christ!