Aluminum fan (10 straight blades) is all one piece. Anything else (11 curved blades) would have a separate belt pulley and fan.
If you have the aluminum fan, the fan removal tool which Ben kindly showed above is absolutely necessary because the fan and spindle are one. The tool is Kirby part T130 and can be had for not much on eBay.
If you have any fan other than the aluminum one, it is possible in some cases to hold on to the fan blades themselves with work gloves or a rag and then twist off the separate, reverse threaded belt pulley. However, it sounds as thought your pulley is seized on too much for you to be able to do that, so you most likely need the T130.