Hello Mr. Hamilton,
Is it a sin to hurt the earth? Are Christians supposed to take care of the earth and the environment?
The difficulty in answering your question is that your are using terms that mean different things to different people.
For example, it is wrong to hurt people, but doctors perform surgeries, which injure people, in order for the people to get better. What looks like harm on the short-term is a benefit in the long-term. In the same way, God has hurt the earth while punishing mankind, such as what happened with the Flood. God did not sin in doing so. The earth is a tool in God's hands and one day it will wear out. "You, LORD, in the beginning laid the foundation of the earth, and the heavens are the work of Your hands. They will perish, but You remain; and they will all grow old like a garment; like a cloak You will fold them up, and they will be changed. But You are the same, and Your years will not fail" (Hebrews 1:10-12).
Some people think any changes to the natural environment is harmful. Yes, mankind is to care for the earth. "You have made him to have dominion over the works of Your hands; You have put all things under his feet, all sheep and oxen - even the beasts of the field, the birds of the air, and the fish of the sea That pass through the paths of the seas" (Psalms 8:6-8). However, it is a mistake to think that nature operates best when left on its own. Good management of the resources makes the earth operate better.
The problem is that in the extreme, some put the earth and the environment as their gods. This is why you find people who think it is wrong to shoot an animal to protect a human life. Animals are living creatures, but they were not made in the image of God as man was (Genesis 1:27). Man is not to do needless harm. "A righteous man regards the life of his animal, but the tender mercies of the wicked are cruel" (Proverbs 12:10). But between an animal and a human life, human life is a superior concern. "Surely for your lifeblood I will demand a reckoning; from the hand of every beast I will require it, and from the hand of man. From the hand of every man's brother I will require the life of man. Whoever sheds man's blood, by man his blood shall be shed; for in the image of God He made man" (Genesis 9:5-6).