On one hand, God states this in Genesis 9: 3—“Every moving thing that is alive shall be food for you; I give all to you, as I gave the green plant.”
On the other hand, in Leviticus and Deuteronomy, God places restrictions on certain moving things as clean and unclean to eat.
There are two things that cross my mind concerning this seeming contradiction. One is speculative. The other is factual.
First, the speculation. It could be in Genesis 9: 3 that God is not saying everything that moves shall be eaten. Maybe I’m being convoluted in my reasoning, but could it be that God is simply saying that humans will look at or consider every moving thing to be consumptive because of mankind’s God-given dominion?
More than likely, though, the verse literally means what it says. But most of the time, we can’t make doctrine based on one verse. The fact of the matter is that God adds a “but” to His statement, starting at verse 4— “Only you shall not eat flesh with its life, that is, its blood.”
Genesis 9: 3 isn’t God’s complete statement about food. The food topic must include all of God’s view on the matter. If done that way, we can see that, yes, all moving things are available. That doesn’t mean, however, that all are good to eat.
Most of the restrictions that God puts on food – beginning in Genesis 9: 4 and that continue in Leviticus and Deuteronomy – are His warning about that which is bad for our health.
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There are more observations about God’s take on other aspects of food in my article What Does the Bible Say About Food? Click here.