Genesis Chapter 1; Verse 26:
 ...Let them (man) have dominion over the fish...birds..animals..creatures...
Genesis Chapter 1; Verse 28:
God blessed them (man) and God said to them: Be fertile and multiply; fill the earth and subdue it.* Have dominion over the fish of the sea, the birds of the air, and all the living things that crawl on the earth

Not sure how this: “we belong to Nature; nature doesn't belong to us” reconciles with the above illustration set in Genesis. But, as Pope Francis has illustrated time and time again from his writing about the earth being our home. And, in protecting life from contraception to natural death leading on the importance of the environment (i.e. our home.) You can imagine that the wrongs which man does has much to do with sin: “Thou shall not kill.” His point is harm you do to your neighbor stems from man’s fall. And, what you do sinfully not being a good steward of one’s home (i.e. environment), your neighbor suffers (especially the poor.).