Do a limited amount of research into deep ecology, find the best argument you can for it and the best argument you can against it, determine logically which argument works and which one doesn't, and write a paper explaining deep ecology, both arguments, and why you think what you think. Make sure the first sentence of your paper is your thesis.
Start by looking up "deep ecology" in our textbook, and seeing what our author says about the arguments for and against deep ecology..
Then look in http://en.wikipedia.org/wiki/Deep_ecology and see if you can find arguments there.
Other places you can look are:
Michael Asher's Deep Ecology Website
Ecophilosophy, Ecosophy and the Deep Ecology Movement: An Overview
Social Ecology versus Deep Ecology:
This is the only anti-DE site I could find. If you find another one, please let me know.