I can't play split-screen on Minecraft XBOX 360 version?

Do you have the resolution set to 720p or 1080p?

So ok try this make sure both controller's are on and make sure each of them are sign in into a profile than 1st player start a world or load a world. Then once the world is loaded 2nd player should press start and then it might ask you to do it again then it should change to split screen. Hope this helps.