I'm not sure how it works, I can only speculate as others have. Perhaps it something in the adhesive along with the corn being covered and perhaps suffocating for lack of oxygen.
I used the Duck tape Max because I remembered reading somewhere here that the cheap dollar store duck tape wouldn't work. It was hard to get a piece to stick, but I persevered until I got it to adhere and only replaced it when it had come unstuck all around. I would then carefully peel it off and apply another piece. I never tried to pull the corn out even when it was at the stage the picture was taken. I didn't want there be a chance a piece be left behind and start growing again. I came home from work a few days after I took that picture to find both the tape and corn gone from his toe. One time I soaked his foot, which some have mentioned doing another time I applied a 40% solution of salicylic acid. Both times after doing so it took several days before I could get the tape to stick again.
I hope this is the last corn I deal with, but if not the duck tape method and a little patience will always be the first thing I try. I would encourage others to do the same.