The parties end up defining themselves by being different from the other party. If one party is for X, then the other party loudly proclaims that it's against it.

This is the exact opposite of what happens. The parties in a two party system move together towards the "median voter." Eventually both parties become the same, not opposites. A proportional representation system encourages polarization because when a party does not win a majority of the seats in the voting body it must compromise with smaller parties further to the right or to the left of it.