John Calvin Commentary Genesis 9:10

"and with every living creature that is with you, the birds, the cattle, and every beast of the earth with you. Of all that go out of the ark, even every beast of the earth." — Genesis 9:10 (ASV)

And with every living creature. Although the favor which the Lord promises extends also to animals, it is not in vain that He addresses Himself only to men, who, by the sense of faith, are able to perceive this benefit. We enjoy the heaven and the air in common with the beasts, and draw the same vital breath; but it is no common privilege that God directs His word to us, from which we may learn with what paternal love He pursues us.

And here three distinct steps are to be traced.

1. God, as a matter of present concern, makes a covenant with Noah and his family, so that they would not be afraid of a deluge for themselves.
2. He transmits His covenant to posterity, not only so that, by continual succession, the effect may reach other ages, but also so that those who would later be born might apprehend this testimony by faith and conclude that the same thing that had been promised to the sons of Noah was also promised to them.
3. He declares that He will also be propitious to brute animals, so that the effect of the covenant towards them might be the preservation of their lives only, without imparting to them sense and intelligence.

Hence the ignorance of the Anabaptists may be refuted, who deny that the covenant of God is common to infants because they are destitute of present faith. It is as if, indeed, when God promises salvation to a thousand generations, the fathers were not intermediate parties between God and their children, whose office it is to deliver to their children (so to speak) from hand to hand the promise received from God.

But those who withdraw themselves from this protection of God (since most people either despise or ridicule this divine covenant) deserve, by this single act of ingratitude, to be immersed in eternal fire.

For although this is an earthly promise, God intends for the faith of His people to be exercised, so that they may be assured that a sure abode will, by His special goodness, be provided for them on earth, until they are gathered together in heaven.