When you allow crossover voting in the primaries, it makes for some nasty little tricks.
For example, let's say party A has a strong incumbent with no real challenger, and party B has a weak challenger that could not beat the incumbent and a strong challenger that could beat the incumbent. So, if party A voters are allowed to crossover, they can vote for the weak challenger, giving their strong incumbent a cake walk if they are successful, or at least causing a rift in party B.