The rules reference says
QuoteAt the start of the turn, a survivor can equip items from his or her inventory or exchange any of his or her equipped cards with cards from his or her inventory.
There are two interpretation of "exchange any equipped cards with cards from inventory"
- Two cards must be actually exchanged (e.g., to unequip my armor, I must swap it with different armor from inventory)
- Any equipped card can be moved to inventory and vice versa (within limitations of inventory size and equipment slotting)
Normally, I would assume the answer must be interpretation 2. However, this make the BoS Outcast very powerful early game, because the survivor can unequip their armor to regain full movement, then re-equip for encounters and fights. This comes at the risk of being attacked without the armor equipped during enemy activation (and possibly dying and losing it), but it's a small and manageable downside compared to having 2 armor and effectively full movement.