I have always understood this as follows:

Each church has to make decisions for its own life as if it were the church catholic — i.e. without constantly referring to other churches. In this way it is not simply a part of the church catholic, but it is the church catholic.

At the same time this has to be held in tension with the fact that it is not the whole church catholic unless it is in fellowship with other churches.

Like all things which need to be held in tension this is frequently a source of trouble.

Of course I am sure that this is not the only way this can be interpreted or understood.

I cannot become enthused over denominational and church ecumenism. Allow me to qualify why by responding to the following quote;

“Each church is the church catholic and not simply a part of it. Each church is the church catholic, but not the whole of it. Each church fulfills its catholicity when it is in communion with the other churches.”

I would rather suggest that; “NO church/denomination is the church catholic…”. Each person must become part of that community by Faith in Jesus Christ alone. Though there are members of the catholic/universal church in many churches from many denominations, the True members would be a drop in the bucket when compared to the nominal members. Though I will not be doctrinaire about this assumption, I cannot convince myself to assume otherwise.

When I analyze contemporary Christianity, I am faced with the following questions;
Where is the Truth as found in the New Testament?
In most churches and homes, in a closed Bible.
Where is the knowledge of that Truth? Luk 10:21
“… thou hast hid these things from the wise and prudent, and hast revealed them unto babes: …”
Where is the faith described in Hebrews?
Where is the faithfulness as practiced by the New Testament church?
In the few who believe and follow.

What is called the church is essentially a mixing pot of pop and traditional cultures in the guise of Christianity. Generally speaking, the candlestick has long been removed from denominational Christianity, only to be found in a few individuals scattered far and wide across the globe. I don’t have much trust in, and don’t see much hope for the contemporary church. My only hope is in Jesus Christ. My hearts cry is; Rev 22:20;
“Even so come Lord Jesus”.

Great quote.