Trying it clockwise definitely put you in a bind. It's best to either look it up or use some thought when you're not sure of threading direction. As the same tool is used for both crank arms the extractor threads that the cap threads into have to be the same on both sides.

If it's plastic you can just break it and take out the pieces, or you can drill two holes the correct size and use a pin wrench to remove. Those are the methods a shop would use. But you can also try a penetrant that's better than WD-40.