Observe, both a burnt offering and a sin offering were enjoined, the one to denote GOD'S mercy, the other man's demerit. Psalms 51:5.
Related Commentaries of Leviticus 12:6
Leviticus 12:6
6 And when the days of her purifying are fulfilled, for a son, or for a daughter, she shall bring a lamb of the firsta year for a burnt offering, and a young pigeon, or a turtledove, for a sin offering, unto the door of the tabernacle of the congregation, unto the priest: