Almost everyone has an ex. There were reasons that you and your ex got together. Attraction, lust, interest, or a sharing of the minds. Something put you two together. Chances are, even though things did not work out, that attraction is still there. Or you would not want to remain friends. In all reality, it is possible to remain friends after being so much more, but it is not recommended.
You are still attracted
The fact that people wish to leave their relationship on good terms is a good rule to live by. However, being friends, seeing each other on a regular basis, is asking for trouble. Chances are that one, if not both, of you, still feel some form of attraction toward the other.
Seeing each other would be tempting fate. All it takes is pushing the common sense aside that one time. Then you are either back in the relationship you want out of, or you are tearing yourself up for being "weak". Neither choice is particularly appealing.
Moving on
Other problems could arise from the ex-lover friendship when both parties move on. There has yet to be an accounting where the new partner has not managed to pick on to something between ex-lovers. It is almost like they can notice the pheromones or something.
If you spend time regularly with the ex, chances of your new partner leaving increase. Even though there might be nothing between you and your ex now, your new partner still senses something. Most of the population will not talk about past romances, which leaves your new partner in the dark. Some partners are afraid that the ex will "own" a part of you that the new partner can never claim.
Just under half of people in relationships will cheat on their partners. That is in their lifetime. Most people learn from cheating and usually will not commit the same offense twice. However, others enjoy that little chance that they could be caught. They love having multiple sources of entertainment.
Sadly if your new romance has been cheated on, they will be wary of being cheated on in the future. You might as well say goodbye to your ex-lover friendship at that point.
Rehashing
Eventually, in the friendship, you or your ex will bring up the past. This is never pretty and happens in almost every ex-lover friendship. For some reason, they will want answers. Or maybe you do. Either way, the past is brought up and suddenly you are forced to either rehash it, or lose the friendship. Losing the friendship will be like breaking up a second time. It is never pretty.
Reforming the relationship
Most often, ex-lover relationships end up being a means to reform the relationship. This is probably the most influential reason not to maintain a friendship with an ex. They may claim to fix their problems, and you yours, but once you get back into the swing of things, you both will start in on old habits. Only in rare occasions does the relationship work out after being friends.
The perfect friendship
While making a romantic relationship work after having an ex-lover relationship is rare, having the perfect ex-lover relationship is much rarer. At some point, people wish that they had maintained contact with an old flame. Most people will envision having the perfect ex-lover relationship.
However, this is not the perfect world. Things do not always work out the way people want them to. Often times, it is just a matter of opening up old wounds at a different time. Or maybe dealing with the pain later than at that moment.
In the end
Having an ex-lover relationship might work for some people, though the number would be very small, it will not work with everyone. Most people do not want the relationship to end and seek that second chance. They think that by maintaining a "friendship" they will have that opportunity. In the end, friendship between ex-lovers is just a way to pretend that things are ok when they are not. At the end of the relationship, you will be right where you started. Wishing for more.