Why would a residential generator panel switch and interlock the neutral?

[ricardocello]

So if the blue arrows represent an open breaker, and that breaker is rated for 120v, does two power sources bonded by their neutral expose the open breaker contacts to 240v potentials, potentially exceeding the breaker's voltage rating?

Note: I tried to fix my math in my post above for correctness.

After 416.666 seconds, the two independent power sources will be 180 degrees out of phase with respect to the neutral, and
the voltage measurement across them would be 240V rms. But the breaker would have tripped long before you get to that if it were closed.

<Now waiting for Tim to drop the in-phase vs. 180-degree reply... >