There is magnetic leakage from primary to secondary and between both half-primaries to each other. When the current in the primary is driven to be discontinuous, you get inductive kickback from the leakage inductances in the form of a voltage spike.
This voltage spike can punch through insulation or flash over sockets, and the spike is sitting on top of B+, so it's got a head start for a flashover to ground. If the punchthrough was one time, it wouldn't be a problem, but the burning residues inside the transformer make punchthrough easier at the same point on the next cycle, and eventually erode the insulation to make a conductive path between layers. The sound goes south, and with an intermittent short you can get a permanent short, or the wire can burn though to give you an open there, and now you have a dead transformer.
So how much loading is too high? For a well designed (equals interleaved, tightly coupled, low leakage inductances, like a fine, high quality hifi) OT, you can easily withstand a 2:1 mismatch high.
For a poorly designed (high leakage, poor coupling, not well insulated or potted) transformer, 2:1 may well be marginal. Worse, if you have an intermittent contact in the path to the speaker, you will introduce transients that are sharper and hence cause higher voltages. In that light, the speaker impedance selector switch could kill OT's if two ways - if it's a break before make, the transients cause punch through; if it's a make before break, the OT is intermittently shorted and the higher currents cause burns on the switch that eventually make it into a break before make. Turning the speaker impedance selector with an amp running is something I would not chance, not once.
