Often when we break up with someone, we really miss their company. The joke that nobody else would get, the information that nobody else would appreciate. You have a history, and that can be difficult to just throw away.
There has been a lot of research done on opposite-sex friendship, and whether it's possible or advisable. After all, very often there is always that sexual tension that always exists between a man and a woman. It IS possible, if you both wanted to... But you just don't acknowledge it or think about it.
Some people find it too difficult to be friends, at least at first, because they are so attracted physically to the person, they wouldn't be able to just be friends. Compliment or insult..? It probably depends on the intent behind it ;)
Others would feel like they were cheating on their current partner if they maintained a friendship with another woman, particularly an ex. Indeed if one is to avoid the mud, one stays out of the paddock ;) Putting yourself in a situation or location where cheating could occur, is usually a very bad idea. Like an alcoholic who avoids pubs and bars, stay away from situations and people which might lead you to conduct you will regret...
Let's face it, maintaining a friendship with an ex-lover is in actual fact keeping the door open, even just a tiny sliver..
Quitting 'cold-turkey' can often be the best way to break any kind of addiction. Which just draws out your pain. Or theirs. It can also prevent you from moving on and meeting someone else, or at least being fully present in your next relationship. And they deserve 100% of you. So in these instances, no, friendship with an ex is not a good idea. When you can think of them kissing someone else and feel nothing, then perhaps you would be ok if you ran into them somewhere.
There's just no easy way to lose someone you love, or even were attached to and accustomed to. Remaining in contact can just complicate things. Men have a harder time than women with this, as they are biologically conditioned to find the one who will procreate with him alone (even though he is also wired to procreate with many...) So he is compelled to chase the one who is more difficult to get - ie the unavailable 'friend'. And the longer the hunt, the more 'feel good' hormones are released, the more high he becomes, and the harder he falls for her...
Unless you really feel nothing for each other (in which case why were you even together?), then break it off 100% for at least 6-12 months. No calls, texts, emails, chance-meetings, messages through friends, nothing. Drop off the face of the earth. Happy healing.