Certain games just don't warrant the inclusion of multiplayer elements. Great examples would be a Final Fantasy, Assassin's Creed, or any other where the addition of another player can destroy the game's story and depth by increasing how many people have to become involved.
Army of Two is a good example of a game that not only warrants, but DEMANDS a multiplayer option. Obvious examples would be other FPS, strategy, or sport games. But certain, story-driven RPG and action/adventure games can be ruined by including other players.
And for crying-out-loud, if you're going to include both split-screen and online multiplayer options, would it kill you to include the ability to do both at the same time!?