To me, a "denomination" is a part of the whole. Full stop. It doesn't have to recognize itself as such. Nor does it have to be organized above the congregational level and have a statement of faith. These things are often true of denominations.
Using this simple definition, let me show you how I've concluded that the Church of Christ (big "C", Sign-Out-Front) is a denomination.
Imagine a young man in the dark jungles of interior Africa. He's never seen a white man, has no idea of modern civilization, has never heard a radio or seen a TV.
All his life, every Thursday evening, the tribe gathers around for a worship meal. They sacrifice a small animal, and roast it, and each community member eats a small piece of it in a ritual. They interpret this ritual as a means of gaining the characteristics of the animal (if it was a rabbit, they gain speed and agility; if a wolf, strength and cooperation; if a snake, ghost-like movements; etc). They also place a drop of blood from the animal into a common water container, and then all drink a small sip from the water. In this manner, they become one with the spirits of the world. After the meeting, they sing and dance around the fire, in honor of all the gods of the earth, and especially in honor of the Great God above all the other gods.
One day, this young man is out hunting, and he comes across the dead body of a white missionary. He's never seen a white man, but he remembers stories from his youth of God-men coming to Earth as messengers, to deliver knowledge to humans. He recalls that in the stories, these God-men had bodies that glowed white with light. He concludes this dead missionary must be one such messenger. Searching the body reverently, he finds a small book, amazingly enough, written in the language of a neighboring tribe, which this young man understands. He takes the book, and begins to read.
From the book, he learns that the Great God created all of the heaven and earth, and all the animals, and even the first ancestral humans from whom all humanity is descended. He learns other history, and even recognizes the story of Noah and the Ark as being very similar to the story of his own people, and realizes that the stories refer to the same event, only his story must have become corrupt over the generations (after all, it would be presumed that the "God-Man" would have the correct version of the story as part of his message to humans).
He continues reading, and realizes that much of his beliefs, while floundering near and about the one true God, missed it in so very many ways.
He learns that God sent a very special God-Man to Earth, one that was in essence the Great God Himself, in human form. The young man doesn't understand all the nitty-gritty details, but he does comprehend a basic understanding that this Jesus is the Son of the Great God, and that like the animals they sacrifice every Thursday evening, Jesus was sacrificed, but his sacrifice does so much more, in that it opens a renewed relationship between humans and the Great God.
Further study reveals that if the young man accepts this fact, and believes and confesses to it, and changes his mind to start worshiping the Great God and his Son as found in this book, rather than worshiping according to his life-long understandings, and if he's immersed in water for a cleansing and a renewal, he will emerge from the water as a new person, saved before the Great God of the book.
He does so.
My question: Is this young man now a Christian?
I'm going to assume you'll say "yes", even though this young man still has a very incomplete understanding of the ways of Christianity.
Now, come Thursday evening, this young man joins his community for worship, but now, instead of worshiping the gods of the Earth, all his activities are oriented toward giving worth to the Great God of the book, and His son, the God-Man Jesus. The young man still participates in the sacrifice, and the eating of the roasted meat, and the drinking of the blood-tainted water, and the dancing and singing around the fire, but he does so giving worth to the real God, not toward the gods he formerly worshiped.
My next question: Is this young man still a Christian?
Yes, he's worshiping incorrectly, out of ignorance; that's plain. But does that "un-make" him a Christian?
It seems to me that he's a Christian, a member of the church of Christ, the church we read about in the New Testament. He doesn't LOOK to us like a member of the church of Christ, but if I understand the conversion process, he is indeed a member of the same church of which I attend every Sunday and Wednesday. Hopefully, as he continues studying, he'll learn more and more of the Biblical way of worshiping.
Now, one last question: What if instead of being in the dark jungles of Africa, this young man was raised in the Baptist church? At some point in his young adult years, he decides to read the Bible, realizes that what he's been taught all his life is not Biblical, decides to be immersed in water to have his sins washed away and to become a Christian, and asks his Pastor do immerse him. The pastor says he'll immerse him, but not for the forgiveness of sins; the young man replies, "Just immerse me; your reasons don't matter; mine do." So the young man is immersed. Is he now a Christian, a member of the church of Christ? If so, if in his ignorance he still attends the Baptist assembly the next Sunday morning, and still worships in form as the Baptists do, does that "un-make" him as a Christian?
Now perhaps you haven't come with me to the same conclusions I have drawn, but if you have, then it must be asked, "Is it possible, at least theoretically, for a Christian to be 'hidden' in some non-Church of Christ denomination?" If so, then the "church of Christ" is larger than the "Church of Christ"; thus, the "Church of Christ" is a part of the whole, thereby making it, by definition, a denomination.
All Christians everywhere, in the dark jungles of Africa, or in the confused trappings of a Baptist assembly, are members of the church of Christ, even if they are not members of the "Church of Christ".
Of course, you may put more requirements on becoming a Christian than I have laid out here. Perhaps you insist that a true convert have proper understanding that he can't wear any non-Biblical name (such as "Episcopalian" or "Methodist"), or that he have a proper understanding of acceptable worship forms (no women speaking in church; the "Five Acts", etc), or that he have a proper understanding of church organization (multiple pastors, multiple deacons, congregational autonomy, etc). If that's the case, then you essentially require a person to convert to a system rather than to a person.
Maybe I've just wasted a bunch of bandwidth with these what-if scenarios, but hopefully they help demonstrate how it is that although I believe the Biblical church of Christ, as found in the New Testament, is not a denomination, the group we generally consider as the "Church of Christ" is, at least theoretically.
If there are any Christians hidden in denominations, we need to call them out, to be "just Christians"; not "Baptist Christians" or "Assembly of God Christians" or even "Church of Christ Christians". We need to drop the descriptive and divisive names; christians who meet in a building with a Church of Christ sign-out-front should alternate their signs every week with other Biblical descriptions; there's nothing wrong with the term "church of Christ" when it's on an equal level with other equally Biblical terms for the church, but when it becomes the "official" term by which our group is distinguished, we have, in
essence, become a denomination.
Lots of words; probably very little value; my apologies for being so long-winded. Hopefully it'll convey the meaning I intended.