More than a few forum operators don't like arguments with Mods, particularly if the subject of discussion is forum-related. These battles about "why did that post get deleted" or "why did ___ get banned" can turn messy and turn an otherwise good community into fighting camps. (This forum's TOS specifically forbids discussion of mod actions in the forums, for good reason.)
If you have been a good member of the community and still want to get back in, just write a note to the admin/owner & indicate your intention to play by his/her rules. Depending on the forum mod structure, it could be that a lesser power banned you - maybe even who you were arguing with.
If you feel alienated by the banning, though, it's time to find a different community.