John Wesley on Leviticus 3:1

A peace - offering - This was an offering for peace and prosperity, and the blessing of God, either, obtained, and so it was a thank - offering, or, desired; and so it was a kind of supplication to God. A female - Which were allowed here, tho' not in burnt - offerings, because those principally respected the honour of God, who is to be served with the best; but the peace - offerings did primarily respect the benefit of the offerer, and therefore the choice was left to himself. Burnt - offerings had regard to God, as in himself the best of beings, and therefore were wholly burned. But peace - offerings had regard to God as a benefactor to his creatures, and therefore were divided between the altar, the priest, and the offerer.