Very briefly, since I must be about my business..you do well to use the lower case c - catholic because that means "universal." Which relates to what was believed by everyone in every place. Of course, Arius stood up and had to be slapped down.
Suggest to perhaps lay aside the frustration noted in engaging the argument. Gain some more understanding of the neutral facts of the history and the issues involved and the possible consequences of unchecked error and let your own mind grapple with that.
For me lower case simply means I give less significane to the church, as catholics represent themselves as the one and only true church...which we know isn’t true.
I do not believe catholic means universal as catholics do, and for that matter what others might believe or want it to mean ‘with regards to church’....rather it’s prefered today that the “Body of Christ” be used, as it’s written, which includes ALL believers who are in Christ.
Additionally....If one adheres to the “Universal Church” language then that does lend one to flow along with the ‘One World Church’ we are warned about...which today often signifies itself as the “Universal Church”.