@Jane391 - Airbnb is set up to be host-centric (profile), not property-centric (listing). It is set up exactly to be one profile for multiple listings (the profiles are the "accounts". The properties are not). If you are currently sharing a profile with your son, you need to set up 2 different profiles - one for you and one for him. Then you need to be made a co-host on his property to be able to manage it. Then when you list a property on your own profile, regardless of your co-host status with your son's property, it is only accessible by you.
In other words:
You have your own profile. That profile will have a property listed on it (the one you want to add) and you alone will have access to edit and manage that property. You will also have permission, given by your son, to manage his listing as a co-host with whatever permissions he's allowed you to have to help him co-host.
He has his own profile. That profile will have a property listing on it (the one you currently have listed) and he will have access to that property to edit and manage. He will also have allowed you as a co-host to manage it in whatever way you've both agreed.
He does not have access to your profile (nor be able to edit it) nor will he have access your listings on your profile unless you make him a co-host of that listing.