As a moderator of a freecycle group there are several things that can be involved here.
1- The email address you are using was hacked and created spam at some time and you never replied tht you had changed passwords. Banning is not actually the right response on their end but not all moderators/owners are technically expert enough to know that the email address the spam seems to have come from if normally a hacked account (typically a webmail account might add).
2. The group sent out a note requiring a response as they cleaned inactive members and you did not reply i the timeframe (normally Ban would not be used here).
3) You used reply to group instead of reply to member then sending that note to the entire membership (could be 25,000+ people in some areas, 5,000 in mine). We use moderation settings here for that but some really large groups call that a critical fail and permanently ban the email address of the user over it.
What you can do is use a new email address and send a note to the owner and ask them what seems to have happened. They can then remove the ban on the other email address once it is resolved.