While your panel could really be wired incorrectly, it also is possible that it is a "split bus" in that most/all of the 240 volt circuits have no main disconnect but the 120 volt circuits do have a main disconnect ahead of the individual circuit overcurrent protection. The result is that disconnecting all loads in the panel might require operating up to 6 circuit breakers. The NEC in 1984 changed so that split bus is no longer used for new installations but existing split bus installations are not required to be changed so long as they are in good condition.

As BUS points out "MAIN LIGHTING" is a common label for the feed to the "bottom" half of these split bus panels. (The assumption is that the other stuff on the "top" half are things like stoves, dryers, and other larger loads).

On first reading I took this to be multi-wire branch circuits where two hots go out and one neutral returns. If the two breaker handles are tied together both would be switched on or off. This would account for the mention of the swimming pool pump.

Just my take.