Question: Why did Jews stop making animal sacrifices?
Answer: From the time that Cain and Abel made the first sacrifice to God, Jews, including Noah and Abraham, made animal sacrifices to God in many places.
When the Jews received the Ten Commandmens on Mount Sinai, one of the new laws stipulated that Jews were no longer allowed to bring sacrifices to God just anywhere.
The Torah says, "You may not worship God in such a manner. This you may do only on the site that God will choose from among all your tribes to place His Name there. You must seek His Presence, and you must go there. You will bring there your elevated offerings, your eaten sacrifices, your tithes, your hand-delivered elevated gifts, your general and specific pledges, the first born of your cattle and flocks...." (Deut. 12:4-6).
Furthermore, "You will not do then what we do here now, where each person does as he sees fit. For you have not yet come to the resting place and to the inheritance which the Lord your God gives you. But when you traverse the Jordan and you settle the land which the Lord your God gives you to inherit, and when He gives you rest from all your enemies round about, so that you dwell in safety, then there shall be a place which the Lord your God shall choose to cause His Name to dwell there. There you must bring all that I command you, your burnt elevated offerings, your eaten sacrirfices, your tithes, your elevated gifts, and all your choice pledges that you might vow to the Lord." (Deut 12:8-11).
The Torah continues: "Watch yourself! Lest you bring your burnt elevated offerings in any place you see fit. Only in the place that the Lord will choose, somewhere from among your tribes, there shall your bring your burnt elevated offerings, and there you must do all that I command you concerning this." (Deut 12:13-14)
Thus, once King Solomon completed and dedicated the Holy Temple in Jerusalem, animal sacrifices were offered only in the Temple. It would be a sin to offer sacrifices in any other place. And once the Temple was destroyed in 70 CE, no more animal sacrifices were offered.