Sheep were used for different purposes. Some sheep were raised to be sacrifices. In the fields just outside the temple, levitical shepherds raised sheep for the passover and for the daily offerings at the temple.
I know that in Leviticus it was a sin to have sex with a woman on her period because blood was sacred then. After the death of Jesus this sacred offering changed because Jesus paid in full the blood and sins of all. The sacrifice is not needed anymore. But my question is.....why sheep?? Why sacrifice sheep? Is it a symbolic gesture of sorts? As in, the lamb of God has been slain for all of humanity's sins? Why were there sacrifices in the first place? Couldn't the people of God in the Bible show their faith in a different way then slitting of throats of lambs? Because in the days of Abraham, his people didn't understand the God (the lamb of God) he was following. I also can't forget (John 1:29 The next day John saw Jesus coming toward him, and said, “Behold! The Lamb of God who takes away the sin of the world!) - DRS81
I never liked the idea of animal sacrifice and it bugged me for a long time being an animal lover. But I eat meat and would be a hypocrite to say I was against the killing of animals when I eat them. Wish there was another way but there isn't unless you go full vegan. It is one of those things that I have to honor God and know he has his reasons for sacrifice.
God's law is there can be no remission of sins without the shedding of blood. Sin is in the blood and in the OT they had to transfer that sin into the animal through the high priest. It's about the transfer of sins, and is a shadow of the transfer of our sins to Jesus. The price of sin is death and something has to pay the price to uphold justice.
If my memory serves me right any clean animal could be used for the sacrifice. It is just lambs and doves made the most sense being readily available. They are symbolic and also tradition. Lambs are symbolic of man's helplessness also. A lamb has no self defenses and won't even run away when being killed. When Jesus came he willingly laid down his life like a sacrificial lamb as a final sacrifice. Any sacrifice made after Jesus' crucifixion is not needed.
God always intended to pay the price of sin with his own blood. Even when Abraham was going to sacrifice his son and God stopped him. God said he'd provide HIMSELF a sacrifice. Many miss the layered meaning there. We serve a God that was willing to suffer and give his own life to save us. But since he was a sinless sacrifice it's like a catch 22. Jesus paid a price he didn't owe and being God had every legal right to take up his own life from the dead and be restored to the Godhead. Since he was also God then he could accept our worship and forgive us of our own sins by taking our place. A kinsman redeemer. There's reason and meaning to every thing God does and if you really get into the issue it'll blow your mind.
There's many great books written on the blood of Jesus. If you want to get into some heavy reading then you'd like those.
Oh also. The story of the 99 sheep and the one that is lost isn't about Jesus love for animals. Although I do believe God loves all of his creations. The story's focus is that God cares just as much about the one lost sheep as the other 99. It's about salvation and how every person is important to God and how he wishes to save us all.