The sacrifice of Jesus christ for our sins?

In the bible it states in more than one instance that God condemned sacrifices. Why than does Jesus dieing on the cross suddenly take away our sins. I'm familiar with the stories and the bible, but that doesn't really explain completely why this had to happen. Why would God contradict himself by denouncing sacrifices, and than sacrifice his own son to form the central dogma of chrisitianity which is that Jesus died for our sins. I don't know but thanks for the help.