A better example of this is illustrated in a talk given by a dear friend. In this talk to an ISM or Autocephalous Catholic jurisdiction, my friend said:
"Like me, you probably are invited to explain yourself when people find out that you belong to a church like this, or worse yet, are some sort of priest! Random inquirers probably misunderstand larger denominations with great regularity, but most of the time, they at least have some idea of what a Methodist or Roman Catholic might be – even if it is a completely wrong idea. But when they meet us, we often blow their categories and they aren’t quite sure who we are or how to understand us..... And most of us reach automatically for stored narratives we have in our pocket, which may have been useful along the way, but may be less so in this moment. The first automatic narrative might be called the inclusivity story, or the “just like… except…” tale... Well, we are just like the Roman Catholic Church, or the Orthodox Church, or whoever, except we ordain women, or gay people, or trans people, or do same-sex weddings.” Or whatever the specifics may be. We hereby set up a game where our vocation as church is only ever seen or understood in comparison or contrast to one of the large denominations. We fail to answer the question or who we are or who we are called to be, without pointing to another church...."
We may feel like it's a "necessary evil" to define ourselves in relation to someone else. As humans, we like to categorize people. If we can place people in a bubble "gay/straight, Democrat/Republican, black/white, etc." we know if they are "on our side." But, I think a better path is to share what we believe to allow the inquirer to discern if they believe it, too. We also can share our rich history to explain who we are and how we got here.
Unfortunately, we belong to a tradition which defies explanation. Most Christians have associated the word Catholic exclusively with the Roman Catholic Church, despite its universal meaning. Despite, as well, its use among other traditions which offer a prefix like Anglo-Catholic, Old Catholic, Evangelical Catholic, or even Eastern Orthodoxy which often uses a derivative of the name Orthodox Catholic Church.
I think the farther we can distance ourselves from mainstream churches in our descriptions, the better it will be. We may be buoyed by the names "Catholic" or "Orthodox" to describe our theological and (especially) sacramental commitments, but we do not have to use them as oppositional words. It is more important for us to build up strong, vibrant communities of faith. Doing this is only more difficult when we base our identity on our opposition to another Christian community. It is also complicated when we seek to change another Christian community, despite our having left it.
I have no interest or desire in changing another tradition, any more than I do by defining myself in relation to it. As I have written multiple times, I wish there were different names to describe ourselves. But we are wedded either by historicity or our firm theological commitments. And these are what should guide us in describing ourselves, not our place in the Christian continuum. I will stand by using Catholic because that's what I am. Not because it's in relation to a larger version of Catholicism but because I am part of the universal tradition--the One, Holy, Catholic, and Apostolic one.
"What a heavy burden is a name that has become too famous." - Voltaire