Maimonides regarded sacrifices as a means of leading Israel to abandon the ways of the environment and cleave to God alone.
Animals were deities – sheep were the gods of Egypt, cattle the gods of India, and so on. The ideal would have been an instant command to cease all idolatrous practices forthwith, but gradually weaning the people off such usages seemed better.
Sheep and cattle could remain in the worship system, but they were to be visibly subjected to God’s rulership.
Abravanel backed Maimonides by quoting a Midrash that said, “A king saw that his son was enjoying forbidden meat, so the father said, ‘Let him eat at my table and he will give up that bad habit’.”
Other commentators profoundly disagreed; Nachmanides, for instance, said that the sacrifices were part of the mystique of the heavenly realms.
When we have no Temple or sacrificial system, however, we have other means of coming closer to God, especially by deeds of love and compassion.