Like my first car's driver's side lug nuts (1970 Dodge Coronet) or the left pedal on a bicycle, it seems that the toilet flush handle, at least the plastic one on our 25 year old paleo-low-water-consumption-toilets has a left hand thread. I noticed this when I replaced the first toilet handle about a year ago. This morning I did the other one. Amazing how easy the plastic nut is to get off when you haven't first been torquing the crap out of it (so to speak).