Those things can be a little aggravating until you learn how to remove them.
I have the wedge pedestal and I have to lift the little lever and then use a side to side rocking action to get mine out. I bend over and grip the seat with my forearms, grab the pedestal with one hand and lift the lever with the other hand, then I rock the seat and pedestal side to side with my forearms. They'll never come out just pulling straight up, you'll throw your back out before those darn pedestals will come out of the base if you just pull straight up.