After decades of use, Revere Ware pan handles can get pretty gunked up. And the screws inside can rust together, or get bound together with greasy gunk. Our to-to method for removing old handles was to hit them with a hammer to break them, and then pry the pieces out, to expose the screw and nut, which could then be removed with pliers. This of course assumes you don’t want to save the old handle.
Reader Tyler offers a quite brilliant non-descructive alternative.
I found a really simple way that won’t damage the handle and is pretty quick and easy. I turn the pot or skillet sideways in the freezer and place the handle on a box so it will rest horizontally. I then put a few drops of water over the female end of the screw assembly (end without a screw slot) making sure the water pools over the head of the screw and doesn’t run off. Then I allow the water to freeze completely solid (about 15-20 mins). After the water is frozen just turn the other end of the screw and if the ice holds the female end of the screw in place it will allow you to turn the screw. This has worked for me on several occasions for screws that will turn freely but both sides turn together, if your screw won’t turn at all then this won’t work. You should also be careful with the handle right after taking it out of the freezer as I would imagine the severe cold may make the Bakelite more brittle, it also would probably not be a good idea to shock it with hot water.