Why is there animal sacrifice in Judaism? Animal sacrifice was found in other religions before Judaism, so could it be that the Jews copied the practice of animal sacrifice from other religions?
First, idolatry did not yet exist. It follows, then, that the offering are not a mere concession to polytheism. The offerings antedate polytheism. They are as old as mankind itself, and they are a natural expression of human thoughts and emotions.
He follows this by saying that offering do not have absolute value -- in the very first instance of offerings, we find that one is accepted, and another rejected. "This gives lie to the notion crediting the prophets with being the first to have taught that offerings have only a relative value."
The next part probably deals the most directly with your question:
It is true, of course, that idolaters, too, offered sacrifices; but, then, idolaters also offered prayers, and we would have to give up a great deal if we were to shun every practice that others have misused.
(Feldheim translation (and emphasis), 2002)
From a skeptical standpoint it would probably be easiest to presume that the ancient Israelites merely adopted and or adapted the methods of worship common at the time their religion emerged but I see no reason that those of us that do not share such presuppositions would find such an assumption that compelling.
Our tradition teaches that although animal sacrifice predates the giving of the Torah it originated with the worshipers of the true God from earliest times (see for example Gen. 4:4) and continued to be a part the way people worshiped God throughout the generations. So based on the traditional paradigm it would seem that as man strayed and began worshiping false deities (I hope to reference the Rambam's elaboration of this process when I can) they took the practice of animal sacrifice with them.