Couple privilege is the advantage that an established couple has, which is especially pronounced when a new person is added to a relationship, whether the new person is dating one or both of them. This is most obvious when the established couple has been together for a long time, especially if they live together, or are married. There is no way out of couple privilege – it’s just there, giving silent advantages that people consider normal. It is mainly brought up as a problem with “unicorn hunters” or those that enforce a primary/secondary prescriptive hierarchy, but it can come up in any scenario where two people are dating before another person comes into the picture. Even if you’re an egalitarian Relationship Anarchist, couple privilege can sneak up on you when you’re not looking.
(There are some people that completely dismiss the idea of “privilege” as a thing in any scenario, which is a completely different problem, but it definitely still exists. If you’d prefer to call it something else, you could call it “couple advantage,” but it boils down to the same thing.)
In many cases, the way in which couple privilege is most visible is when a new partner starts a relationship with one or both people in an established relationship, and the people in the existing relationship give the new partner a list of rules in a take-it-or-leave-it manner. The couple often gives the reason that if the third person doesn’t like the rules, they are free to leave. This is only one of the more obvious ways, however; there are many smaller ways that are less obvious and sometimes more insidious.
This isn’t to say that couple privilege is necessarily a bad thing on its own, it’s just a thing that is there. Having privilege doesn’t make you a bad person, as it’s just something that happens. It’s what you do with that privilege that matters.