A king cannot capture a king in chess because:
In order for a king to capture a king, the kings would first have to be adjacent to each other. In order for the kings to be adjacent to each other, one player would have to move his king right next to the opponent's king, which would place the first player in checkmate. Because it is illegal to make a move that deliberately places yourself in checkmate, it would be illegal to cause two kings to become adjacent to each other. Therefore, a king can never capture a king -- or more specifically, never place a king in check.