Good sportsmanship, should you have to shake you hated rivals hand, why or why not?

In sports there are some very heated rivalries. Where one team does not like the other. I will give a few examples Chicago vs Green Bay, Michigan vs Ohio state, The Red Sox vs the Yankees and many more. Should you have to act like you respect your rivals after the game? You hate them all year but after an intense competition you have to be a good sportsman show good sportsmanship why?