No, you’re not, and please quit saying that.
It has become increasingly frequent that we hear members of the body of Christ refer to themselves in that fashion when discussing religion with members of various denominations. Perhaps we are trying to accommodate their language and their unscriptural understanding, but you can accommodate to the point of error and such is the case here.
“I’m Baptist.” “I’m Methodist.” “I’m Presbyterian.” “I’m Catholic.” “I’m church of Christ.”
One of these things is not like the other; one of these things just doesn’t fit. The first four descriptions share certain things in common. They are all denominational identifiers and none of them has scriptural precedent in the designation of the church. The last is added so that we can parallel the language of our denominational neighbors, but the effect condescends the church of Christ to that same level. Maybe we become ashamed of the claim altogether.
We are making some mighty uncertain sounds with language like this (1 Cor. 14:8). Why not rather say simply, “I’m a Christian”? Does that not communicate the truth and perhaps also make a point about our refusal to create or join any new denomination (1 Cor. 1:10-13)? The phrase “church of Christ” is no more ours to trifle with than the honorable word “Christian.” Our denominational friends have almost given up calling themselves Christians, instead preferring to emphasize what “brand” of Christian they are. Do we resist sectarianism for 1900 years and then surrender because it is more convenient and less likely to get us in a messy discussion?
Such has given religion a bad rap anyway. Sometimes hurt feelings result and sometimes bloody noses. But every once in a while conversions result and every once in a while is worth the risk. Moreover, it demands that we be clear in who we are, not bowing to the ungodly language of church dividers.
When the apostles began taking the gospel into all the world, there was exactly one kind of church in all the world. It was the one that Christ promised to establish (Matt. 16:16) and did purchase with His own blood (Acts 20:28). He both built it and bought it and it was His; it was the church of Christ (Rom. 16:16). There were zero denominations in all the world. No church called itself Methodist, Presbyterian, Baptist or Catholic. But friend, no Christian ever referred to himself as “I’m church of Christ” either.
Repeat after me: “I’m a Christian. I’m a Christian.” It’s not hard.