Am I using the crank extractor correctly? I have this X-Tools crank extractor:


  X-Tools crank extractor tool for removing standard Square Taper and ISIS type cranks.




Here's the end that pushes against the crank:



Here's my crank: (it's threaded on the inside, but there's also threading on the narrower bit further in behind the square opening, which my crank extractor pushes against but does not engage with those inner threads...)



I screw in the crank extractor like so:



Then I put an allen key into the crank extractor and try to turn it clockwise, but it's just not budging:



The inner bit of the extractor seems to be pushing correctly against the crank. But do I have the right tools for the job? Am I going about this correctly? Do I perhaps just need more torque than I'm getting off the allen key?

Follow-up

Well, I left what I thought were "dust protectors" off after working on this. During a cycle, my pedal fell off the bike. Here's are a couple of photos for more info:

What I thought were just dust protectors, which keep the pedal screwed in:


View of the spindle after pedal fell off:


The pedal that came off:


Now I have to get the pedal on the drive-side off, and will follow up.
I don't know about this this particular crank extractor, but the one I have came with two different end caps, one for ISIS/Octalink and one for square taper. Check that the end cap you are using fits inside the square hole in the crank, otherwise you will just strip the threads.

After you are sure you have the right tool, use more torque. If you have a piece of metal pipe at hand, use it for extra leverage, or get a longer wrench. Turning clockwise is correct.