If Islam were a tree, the scarf would be one leaf on the same twig with all the guidelines for modesty for both men and women. Muslims believe that God created humans and all their strengths and weaknesses, and he created guidelines for how to best deal with his creations. We believe the attraction between the sexes is a gift from God, but belongs within certain parameters. So Muslims try to act responsibly by making a conscious effort to attract no one except their spouses. Both men and women in Islam, then, are to act modestly and dress modestly.
Women cover everything but their faces and hands.
Men cover from their stomach to their knees, and also should loosely cover their chests. What should be covered in public differs for men and women because what's under the clothing is different. The day I first braved the doors of my high school with a scarf on my head, I did not even tell my parents until I got home. Instead, I wear a scarf because it makes perfect sense to me. I don't see this as oppression, but liberation.