As benhur has pointed out, the capital/small letter distinction didn’t exist in ancient Greek. So that whole line of argument is silly.
On the other hand, I don’t get benhur’s distinction between a “proper noun” and an “adjective.” When we say “the Catholic Church” the word “Catholic” is obviously being used as an adjective. I think benhur means “a proper adjective.” And in English “a proper adjective” means one that is capitalized. Which benhur has admitted ancient Greek didn’t do. So the distinction is dubious.
Of course Catholic/catholic means universal. But what does universal mean?
To hear many Protestants talk, it means “including everybody”? But every who? Not every human being on the planet, surely? Every Christian? But how then are we defining Christian?
Historically, from the beginning, “Catholic” meant “the true, universal Church.” But it was always, from the beginning, set in contrast to other groups who claimed to be Christian. In that sense it was always a “proper adjective” and benhur is just plain wrong. The term first appears in Ignatius’ letter to the Smyrnaeans, chapter 8, whose heading is “Let nothing be done without the bishop.” In context, this is polemic against various other groups claiming to be Christian in second-century Syria and Asia Minor. He is emphatically not saying, “all those other groups are part of the Catholic Church because they believe in Jesus too.”
In the early Church, people who were outside the Church were not considered Christians in any salvific sense–“you can’t have God for your father if you don’t have the Church for your mother.” Then in the third century Rome began recognizing baptisms outside the Catholic Church. But at least in Augustine’s later interpretation, this didn’t imply that people could be saved outside the Church.
Gradually, reluctantly, the Catholic Church has had to admit that yes, people not in full communion with the Church are genuine believers. And yes, that creates some daylight between “Church as body of all believers” and “Church as those in communion with Rome.” From Rome’s perspective, the term “Catholic Church” applies most fully to the latter, but all believers are to some extent members of the Church.