I think this pretty well answers the question as Christians do we have a responsibility towards the earth.
To think that God gave man carte blanche to plunder and destroy the earth is simply ludicrous. He is its Creator! Why would He immediately command Adam to ruin it? Would any woodworker, upon just finishing a beautifully stained piece of furniture, tell his son to break it up for firewood? No! Just as God desires for His creation, the woodworker would put his handiwork to use and also care for it by keeping it waxed and dusted to prolong its life.
This is exactly what God told Adam. Genesis 2 contains a parallel account of creation, adding detail to certain parts of the narrative of the first chapter. Notice God's expanded instruction: "Then the LORD God took the man and put him in the garden of Eden to tend [dress, KJV] and keep it" (verse 15). This greatly modifies the force of "have dominion" and "subdue it" from Genesis 1:26, 28!
Tend (Hebrew 'abad) means "to work or serve," and thus referring to the ground or a garden, it can be defined as "to till or cultivate." It possesses the nuance seen in the KJV's choice in its translation: "dress," implying adornment, embellishment, and improvement.
Keep (Hebrew shamar) means "to exercise great care over." In the context of Genesis 2:15, it expresses God's wish that mankind, in the person of Adam, "take care of," "guard," or "watch over" the garden. A caretaker maintains and protects his charge so that he can return it to its owner in as good or better condition than when he received it.
As for the question as to whether we think we ourselves are capable of our own destruction, I am not sure really. I know that someday (in my belief) (btw--not every christian believes in the rapture)the earth will end and Jesus will come to take the saved to heaven and the lost will be in a fervent heat. Perhaps that heat will be man made, perhaps not. I know it won't be a flood.
2 Peter 3