The same reason they're obsessed with saying the N word. They usually don't want to say the N word even if given the chance. But having other people saying "no, you shouldn't/can't do this because it offends me" offends them greatly. They must have unrestricted access to everything at all times even if they have no desire to utilize those freedoms.

Now, Islam deserves to be criticized just like any religion. But I don't see a point in drawing Muhammad. Most Muslims aren't deranged terrorists, so when you do draw him they're just going to be offended and upset and go on with their daily lives. The only people who will react to your actions in a way that "interests" you will be the ones who are willing to behead you and blow up your home, and even then most Muslims condemn that violence, so you're really just inviting exclusively extremists to harass you for what - internet points?

I don't think the professor should've been fired because they took precautions and it's a historical artifact, but the whole "draw muhammad" movement is just racist white people who are angry at terrorists, and then associating normal Muslims with terrorism just because they don't like being offended and ask them to not do that.