That was really complicated. Let's just say that the two 120V legs are 180 degrees out of phase with the other. Therefore they use each other for the return.
Adriver, you may need a neutral in a 240v service if the device you are supporting requires it. For example a hot tub. Some hot tubs can be wired as either 120 or 240. But if you go with 240, it may still need the neutral to support internal controllers or other devices (blowers, lighting, etc.) that still need to be run on 120v. Some electric dryers need both 120 and 240 too, for the same reason.