My apologies for asking this, but do you know that the pedals have different handed threads? Right pedal has a right-hand thread (ie normal) and the left pedal has a left-hand thread and needs undoing by turning "the wrong way".
Also bear in mind that the thread is handed for the way you screw the pedal thread into the crank. When you are undoing it from the other side it will seem wrong as well.
So, a right sided pedal has a RH thread and would be loosened by turning anti-clockwise. But when being loosened from the Allen socket at the end of the pedal you need to turn it clockwise as you look at the socket, not anti-clockwise. All of this is the other way around for a left pedal, therefore loosen ACW for the left-hand pedal.
Next step, make sure that the Allen key is a good fit. Be certain that you are turning it the correct way. Hold the Allen key in place securely and try again. If it still won't budge, try some penetrating oil on the threads. You may have to leave it for a while to give the oil a chance to do its job, say an hour. Try again, still no luck, then hit the Allen key with the largest hammer you have. Do it slowly and with confidence.
Once you have the pedal off, resolve never to fit a pedal to a crank without first coating the threads with an anti-seize, like Copper-slip.
Reverse thread on left side *plus* it turns backwards from what we expect since we are wrenching on the back side (assuming Allen wrench type) so CW to loosen the right side; CCW to loosen the left. I hesitate to recommend an Allen socket in an impact gun but if all else fails...
We are threading steel into aluminum (usually) so I like to use anti-seize on the threads.
Gripe - with all the digital clocks/watches no one will know what CW/CCW/ACW means anymore but soon no one will work on anything anymore anyway. /gripe/