Aw does not invariably mean free choice. In a particular oath construction, the textbook allows it to convey an endpoint or “until” relationship.
«لا أدخل هذه الدار أو أدخل هذه الدار»
I will not enter this house until I enter that house.
In this historical juristic example, order matters. Entering the prohibited house first breaches the stated sequence; entering the other house first changes the result. Here aw is understood close to hatta, not as an unrestricted selection between houses.