That's pretty silly. Just strike out the parts you don't agree with if that's how you feel.

Is there a reason why one should quit instead of negotiating the contract while also letting them know you are offended by their initial offer? (Of course, if my current employer pushed something like that on me, I would be starting to look around.)

If anything, quitting is likely worse than being let go because you likely have less of a claim with regards to unemployment (a lawyer would need to specify the actual details).