I used the word "extremist" in place of "Muslim" for exactly this reason.

Yes, but depicting Mohammed doesn't just offend the extremists, does it.

I'd rather offend a few innocent Muslims in protest than stand by as Muslim extremists terrorize and murder because of a cartoon or a movie.

What you are suggesting here would do nothing to stop terrorism or murder. All it would do is create hostility and ill-will where there is no need for it. If anything you would be helping to fuel the unrest.

You seem to forget that people are being killed over this. Buildings are being bombed. This needs to stop. The best way to do this is through protest.

And you seem to forget that there is more to this situation than "us versus them". I don't know what you think this protest will accomplish, but I can tell with some certainty what it will do: draw a line in the sand between you and them. Situations like this are entirely dependent on the behavior of those involved. This is not a conflict between the civilized western world and the brutal theocratic east, but it can be if you'd prefer to treat it that way.

I compare Draw Mohammad Day to the Wear Pink anti-bullying campaign. A few years ago, a boy was bullied for wearing pink. The next day, every student in the Canadian school wore a pink shirt. This is the same logic as Draw Mohammad Day. The protesters said, "No. We will not sit idly by as you bully us out of our rights and freedoms."

Except that wearing pink is an inoffensive way to express ones personal taste. Drawing Mohammad for the sake of drawing Mohammed offends people and serves no purpose other than to offend.