Typically happens between people battling for spots at the end of the game: Player 1 is strung out in a line of territories, and can only reach his opponent in one place. Player 2 can bring two or three territories to bear against this one, but can be easily cut by a successful attack from Player 1.

Both seem to win equally often, which do you prefer? All other things being equal, I'd prefer to be the cutter rather than the cuttee. But thats just me.