The issue described occurs due to the settings in the master-detail relationship. Specifically:
The Allow reparenting checkbox, Child records can be reparented to other parent records after they are created, is unchecked (B). This setting prevents changing the parent record (contact) of a child record (service plan) once it has been set. If 'Allow reparenting' is unchecked, it restricts the ability to change the associated contact, leading to the issue observed.
The other options do not directly address the inability to change the associated contact on a service plan record. The 'Read Only' and 'Read/Write' settings (A and C) pertain to access rights to the detail records based on the master record's access but do not affect the ability to reparent a record.
For a detailed understanding of master-detail relationships and their settings, including reparenting, see the Salesforce documentation on relationships:
Master-Detail Relationships: https://help.salesforce.com/articleView?id=relationships_considerations.htm&type=5