The term "Catholic Church" was coined in 106 AD by St. Ignatius in his epistle to the Smyrnaeans...
No one has a problem with the word "Catholic" - as it means "universal". And all believers in the Lord Jesus Christ are of the same body of Christ. No matter where they are or who they are ("Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house..."). The 'disagreement' arises when the Church of the Roman Empire usurps this name to apply it strictly to themselves.
...Christianity thereby became the official religion of the Roman Empire.
It seems odd when reading Acts, and the Epistles, to imagine the simple, God-fearing churches as having 'evolved' into this creature of the Roman Empire - with its purple robes, legions of officers, giant marble cathedrals, gold, and the such... But maybe that's just me...
Why aren't you walking around in sackcloth and celebrating the Lord's day in a clay hut, if the trappings of Rome offends you? God demanded opulence in designing the Ark of the Covenant, didn't He?
Even the Ku Klux Klan? They believe in Christ, too. You consider them part of the body you belong to?
The 'disagreement' arises when the Church of the Roman Empire usurps this name to apply it strictly to themselves.
No one else wanted to claim it I suppose. Maybe the Holy Spirit made them do it?