Most people prefer not to be friends with their exes after a breakup because they feel that there will always be a lingering feeling of bitterness and resentment, which will make the friendship impossible to happen.
If it is a really crappy relationship that ended in a completely shitty breakup, then the idea of being friends with the other person is definitely out of the question.
However, being friends with an ex is not exactly an impossible feat as there are former couples who have managed to stay acquainted as friends even after the relationship is over.