I had an issue taking mine out as well because my trimmer is ancient. I would spray it with a good penetrating oil, wrap the cutter with a towel and use a pair of channel-locks while holding the main shaft in place. You may have to hold the shaft with another pair of channel-locks with a towel wrapped around it. They key to this is not to mar up any of your parts, even the old cutter head as you never know when you may need it again as a temp replacement.
BTW, mine has no set screw holding the cutter head in place. The set screw is in the cutter head which holds the pilot in place, which has no bearing on holding the cutter in place.