The biggest thing to remember is that a pedal always threads so that the pedaling action will screw it *in*, which means that they do not both follow the lefty loosey - righty tighty rule. You may actually have been tightening the pedal rather than loosening it..... (I think it is the pedal on the right - with the bike upsidedown - that threads backwards from normal).
In any case they can just be really tight and difficult to remove. I suggest having a wrench with the longest handle you can find for the most leverage. If the pedal type supports being removed with either/both an allen type head from the outside and a pedal wrench from the inside using both at the same time can help too.