From What Christians Want To Know –

We might think we own animals, in particular our pets, but the Bible teaches that these are not actually ours. We are only stewards of what God’s given to us. God owns “every beast” there is, including your cattle or sheep or oxen or whatever else it is you own, including your pets. In fact, everything “that moves in the field is” God’s, so that included everything. The point is we better think about that when we are caring for God’s creatures, whether great or small.