You should not have to press the drum off the hub.
If it sat a long time they can corrode in place. If the brakes are misadjusted they can bind if the pads are jammed against the drum. If the pads are worn into the drum surface they can be "locked" in, the studs holding the pads to the shoe base can grind into the face effectively tounge-and-grooving the pads into the drum (assuming studded, not bonded pads). Back off the pads as far as you can using the adjuster and you should be able to get them apart.
A few light raps with a rubber/plastic mallet can free some corroded bits, don't whack with a steel hammer you can crack the drum..
