Relationships were built to be reciprocal. We started out with Family / Account relationships. So, if I am your Parent, you are my child. If you are my cousin, I am your cousin. If you are my guardian, I am your ward, etc. That worked well for that purpose and still does.
We later started adding attributes such as HIPAA authorized, Guardian, and Emergency Contact, etc. These are done from the perspective of the client. For example, maybe we have a child client "Mary" who is developmentally and physically disabled. She is likely to make her parent her Guardian and give her parent "Jim" HIPAA authorization to see her records or make her parent her emergency contact. When we look at the parent Jim's record we see that Guardian and HIPAA checkboxes and the emergency contact checkbox are selected, so while we think it is obvious that people would understand that disabled child is not adult Jim's guardian or emergency contact - but that Jim is Mary's guardian and emergency contact, the "ambiguity" of just seeing a checkbox might be confusing for people not thinking about the client-non-client relationships.
In theory, we can change that and add things like tooltips or make the relationships a lot more complex, but we don't really think that is needed, because if you think of the relationships from the client perspective, this does make a lot of sense.
Here is another example, which is more in line with your request: I am a client at Arc Wayne. I live with my boyfriend; my aunt is my emergency contact; my boyfriend has me as his emergency contact. Let's say Arc Wayne found out the client is in the hospital - who do they call?
Answer: When Arc Wayne goes to the client's account and they look at the relationship grid. They see the row for the client's aunt also has the emergency contact column checked. They click on the aunt's ID, and her phone number appears. On the popup they can see additional info. In the below example from our test system, the additional info says that the person is the primary emergency contact.
You can also have a report if you'd like, called 'emergency contacts' or something similar that lists all accounts and their emergency contacts. That way, instead of having to click around in an emergency, they just go to that one report (which can be available as a link on your homepage dashboard or on the menu) and search for the client's name and the emergency contact and the contact's phone# and email will be displayed.