I cannot be friends with an ex for one main reason: it is impossible to go backwards. Even if the relationship is truly over in every sense, you cannot go back to a time when those interactions had not happened. While I have no remotely romantic feelings for any exes, there will always be the recollection of negative experiences that brought the end of the relationship. I don't need or want to be reminded of those things. No matter how terrific a person or great a friend an ex might be, I ended the relationship for a reason. Life has moved past that, and I need to keep it moving forward rather than backward.
In many cases, one or both former partners have moved on to other relationships, and continued interaction can cause emotional difficulty for the current partner. Keeping in touch with an ex isn't worth upsetting the person I am with.