There are five major offerings described in the Old Testament (Leviticus 1-5): burnt, meat, peace, sin, and trespass. One them, the meat offering, does not use an animal sacrifice. The other four do. However, the offerings differ in whether the animals are to be male or female. Here is how they are specified. The burnt offering is to be a male (Leviticus 1:3, 10). The peace offering can be either male or female (Leviticus 3:1, 6). The sin offering is to be male when offered for "a ruler" of the people (Leviticus 4:22-23) but a female when offered for "one of the common people" (Leviticus 4:27-28). Finally, the trespass offering is to be a female (Leviticus 5:6). The question is why.
Most likely, the male is a representative of Jesus Christ--the man Jesus. The burnt offering is a picture of a complete sacrifice and it must be a male. Also, the sin offering for a ruler must be a male. A ruler would be someone like a king, a priest, a judge, or a prophet. Jesus is all of those. The female would represent the common people (as in Leviticus 4:22-23 in reference to the sin offering). Men are often identified in scripture as they who are "born of a woman" (Job 14:1; 15:14; 25:4; Matthew 11:11). The female would therefore be a fit representative of mankind as a whole.
The peace offering could be either male or female because it was a picture of our peace with God and our fellowship with Him and with each other. All are included. The sin offering, which deals with the sin nature, could be either male or female depending on the purpose of the offering. The common man's greatest problem is his sin nature, so the female was used for the common man. However, Jesus, represented by the male for the ruler, became sin for us on the cross. They both fit in different ways. Last of all, the trespass offering deals not with the sin nature as a whole, but with individual sins. Although Jesus became sin for us, He never committed individual sins. The offering must be a female. Always remember that every detail in scripture has a purpose for being there.