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 1:3If his offering be a burnt sacrifice of the herd, let him offer a male without blemish: he shall offer it of his own voluntary will at the door of the tabernacle of the congregation before the LORD.
See All..., 10). The peace offering can be either male or female (Leviticus 3:1And if his oblation be a sacrifice of peace offering, if he offer it of the herd; whether it be a male or female, he shall offer it without blemish before the LORD.
See All..., 6). The sin offering is to be male when offered for "a ruler" of the people (Leviticus 4:22-23 [22] When a ruler hath sinned, and done somewhat through ignorance against any of the commandments of the LORD his God concerning things which should not be done, and is guilty; [23] Or if his sin, wherein he hath sinned, come to his knowledge; he shall bring his offering, a kid of the goats, a male without blemish:
See All...) but a female when offered for "one of the common people" (Leviticus 4:27-28 [27] And if any one of the common people sin through ignorance, while he doeth somewhat against any of the commandments of the LORD concerning things which ought not to be done, and be guilty; [28] Or if his sin, which he hath sinned, come to his knowledge: then he shall bring his offering, a kid of the goats, a female without blemish, for his sin which he hath sinned.
See All...). Finally, the trespass offering is to be a female (Leviticus 5:6And he shall bring his trespass offering unto the LORD for his sin which he hath sinned, a female from the flock, a lamb or a kid of the goats, for a sin offering; and the priest shall make an atonement for him concerning his sin.
See All...). 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 [22] When a ruler hath sinned, and done somewhat through ignorance against any of the commandments of the LORD his God concerning things which should not be done, and is guilty; [23] Or if his sin, wherein he hath sinned, come to his knowledge; he shall bring his offering, a kid of the goats, a male without blemish:
See All... in reference to the sin offering). Men are often identified in scripture as they who are "born of a woman" (Job 14:1Man that is born of a woman is of few days and full of trouble.
See All...; 15:14
See All...; 25:4
See All...; Matthew 11:11Verily I say unto you, Among them that are born of women there hath not risen a greater than John the Baptist: notwithstanding he that is least in the kingdom of heaven is greater than he.
See All...). 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.