This isn't a matter of looking "cool" or "uncool." Its a matter of adolescent growth, finding their own way, pushing the boundaries.  Teenage years are times of conflict, and hopefully both parents and teens can show restraint and get through it.

"Rebelling" against the parents? How clichéd...
Certainly not my forté, but then I found that my parents generally had good advice and was smart enough to know when not to listen to them.

...."Unless their parents are asking them to do something illegal" or their parents should not be allowed to be parents?

I don't think most children do this to look dumb, but they do it because of a natural urge as an adolescent to develop their own identity separate from their parents.

Most teens are not disobeying their parents, their just trying to find their own independence and their parents may not approve of what their doing and this is when disobedience comes in.

Unless their parents are asking them to do something illegal.