This fellowship offering is distinct from the sin offering in chapter 1. Male or female was ok, and only parts of the animal were for God, the blood and the fat.
I bothered to check commentators for this one. They said the fat represented the best of it, giving our best to God, and the blood represents life, giving back our time and whole self to God.
The rest, the meat, was eaten by the priests and the person bringing the sacrifice. Commentators say this was about enjoying, not getting, relationship with God.
Communion brings these both together, remembering Jesus death for our sins and sharing a symbolic meal with other Christians as part of worshipping God.
The commentators also mentioned some practical benefits of the rules. We now know that the fat, which they regarded as a delicacy and giving the best to God, is not the healthiest part of the animal. And the section not eaten was also the repository of parasites. By following this rule, the commentator speculates the Israelites would have enjoyed better health than their neighbours.