The later-model Maytag Dependable Care washers had a little 1/4 screw at the base of the agitator that held it on to the drive shaft. On the older model units, the agitator was held on a bit differently. Academy Fellow Willie explains The Trick™ :

The older Maytag's don't have that 1/4" hex screw in the side of the agitator holding it on. They use a rubber o-ring style band around the agitator shaft that the agitator snaps down onto, it can be very difficult to remove the agitator on these machines without the use of a strap under the agitator looped over a 2x4 to pop the agitator off or the use of the "Agitamer Tool".

Source: Maytag HA806 Series 01 SN 7608722WW Won't Agitate