While I largely agree with the writers who commented before me, I will try to explain my views a bit more gently — after all, I do respect your beliefs, and your attempt to understand and share them in the best possible light.
Most of us who identify with a particular faith like to think that our religion is God reaching down to humanity — and consequently, our rituals and commandments are divinely sanctioned. But unfortunately, there are many different belief systems, and their teachings are often contradictory. So it seems that religion is better understood as humanity reaching up to what we understand as God, in fear, longing, desperation and hope — but without certainty. Our rituals and laws, then, are painfully human and subject to review as we grow, evolve and expand our knowledge.
Animal sacrifice was nearly universal in early religious practices, and it is not difficult to understand why. What do we do if we are trying to win someone’s favor, or if we have perhaps offended someone or hurt their feelings? Our impulse, of course, is to make things right by offering a gift. Depending on the situation, we may be thinking of chocolates, roses or perhaps even jewelry, but the gift has to be proportional to our desire. If you have been caught in an affair, and your spouse has been talking with an attorney, a candy bar from the local convenience store simply won’t do the trick — a $50,000 diamond ring and an apology while kneeling may go farther.
Our ancestors, whose ideas of God were often anthropomorphic, sought to win divine favor (recovery from illness, rain during the growing season, etc.) by offering gifts — that is, sacrifices. And what did they have to give? Since most of them were herders, hunters and gatherers, or subsistence farmers, their wealth was measured by the number of sheep or cattle that they owned, or the amount of grain that they has stored away. And these were the gifts that they offered in the sacrificial fires.
Our knowledge of the universe is vastly different today, and fewer of us see God as an all-powerful being with human-like feelings and impulses. That creative agent which is ultimately responsible for bringing our evolving universe into being is unlikely to be moved by me slicing the throat of another (more innocent) sentient being, such as a cow, a goat or even a chicken. And having been raised on a farm, I know how intelligent and indeed human-like these animals can be. They do not deserve to die, in my opinion, so that you and I can derive vicarious satisfaction from participating in ancient rituals.