Why can't i play minecraft split screen on my ps3?

Because it's not a split screen game it's ethier online or solo

Yo play split screen, make sure your video source is at least 720p. Because Splitscreen requires a screen with an output of 720p or higher, the console's video output needs to be configured accordingly. The video mode can be checked by going to Settings > System > Console Settings > Display - Make sure this is set to 720p or higher.

Local Split Screen play set up:

Step 1. Select play game and choose to either Create a New world or Load a previous world and make sure you are using 720p video.

Step 2. Make sure to uncheck the Online Game box.

Step 3. After entering the world, press start on the controller you wish to bring into the game.

Step 4. Sign in the player who will be using the controller.

That's it! Local split screen can be played with up to 4 players.

For online split screen, do the above and make sure to check the online game box.