Actually, both male and female goats were used as sin offerings during Old Testament times.
The Bible tells us:
"But when you unwittingly fail and do not observe all these commandments, which the Lord has spoken to Moses, even all that the Lord has commanded you through Moses, from the day when the Lord gave commandment and onward throughout your generations, then it shall be, if it is done unintentionally, without the knowledge of the congregation, that all the congregation shall offer one bull for a burnt offering, as a soothing aroma to the Lord, with its grain offering and its drink offering, according to the ordinance, and one male goat for a sin offering." (Numbers 15:22-24)
According to the above verse, when the congregation of Israel sinned against God unintentionally, the congregation was required to offer a male goat for a sin offering, along with a bull for a burnt offering with grain and drink offerings.
But when a person in the congregation sinned against God unintentionally, that person was required to offer a one-year old female goat for a sin offering.
"Also if one person sins unintentionally, then he shall offer a one year old female goat for a sin offering." (Numbers 15:27)
So both male and female animals were used in offerings.
For sin offerings, both male and female goats were used.