I think this is the toughest kind of breakup because the connection is still alive. If anyone has ever tried to break off a branch from a tree, he will recall that it will not only take more time and strength to tear one off a live tree branch, that tear will look ugly and messy. Compare that to a dead tree branch. Snap! goes the branch. Not torn off but just broken off. Almost clean. No tree xylem and rubbery fibres hanging out with tree blood (ok, ok, tree sap) dripping everywhere.
The breakup where mutual love still exists is the death of that live tree branch.