The threads in the pump are for putting the pully ON, not taking it off. There should be just a plain ram nose on the puller, which will pass through the centre of the pully as it comes off (otherwise, it lines directly up on the shaft.)
Expect it to be difficult to remove, I've never had them come off easy. Your pump should come with a bolt, nut, and washer - this is the "kit" to put the pully back on. Paint the shaft and pully hub with never-seez, set the pully hub over the shaft end, and then screw the nut onto the bolt ALL THE WAY UP to the head. Put the washer on.
Thread the bolt into the pump shaft until it bottoms out, then turn the nut and washer until they contact the face of the pully hub. Get out your wrenches.
The never-seez should make it easier to press the pully on, but you'll go until the washer bottoms out agains the shaft nose, and the pully hub is flush with the end of the shaft.
5-90