As to ..."God entrusted creation and history to the covenant between man and woman,"...
I do hope P. Francis is not trying to use the Genesis myth as though it were history. True enough – this is the myth story that expresses our common human experience. Couples reproduce. And humans are responsible for the human effect on the Planet. That is our responsibility before God.

But let's not get it backward. The human experience and thought is the source of the myth, not the other way  around.