Previously, when adding an address to a profile, users always had the option to Add New Address or Select Existing Address. With the October 2016 release, a constituent must have a relationship with all other constituents sharing an address in order to have the shared address added to their profile. The option to Select Existing Address will be unavailable if the constituent does not have a relationship with all constituents sharing the address.
For example: John Doe and his son, Jack Doe, share their Home address. John also has a spouse relationship for Jennifer, Jack's step-mother, but there is no relationship set up between Jack and Jennifer. When attempting to add John and Jack's shared address to Jennifer's profile, only the option to Add New Address will be available. In order to add John and Jack's existing shared address for Jennifer, she will need a step-parent/step-child relationship to Jack.
To make the option to Select Existing Address available, review the shared address to determine who is currently sharing it. Then ensure there is a relationship between each of those constituents and the constituent you are adding the address for.
To determine which constituents are sharing an address, hover over the sharing icon next to the address type.