I should clarify that my position is that I use AD/BC in everyday speech, but if I had to actually publish something public facing, I certainly would use the CE/BCE system for the obvious reasons. My objection to you was not that using the system is bad, but that it's a trivial thing and therefore (by my attempted implication) an annoying and pointless thing to try to "correct" someone on.

So I did actually read the link, and I didn't know all of the history, but I did have pretty good familiarity with modern Discourse about it as the article outlines. I would say the only compelling addition is this:

Roman Catholic priest and writer on interfaith issues Raimon Panikkar argued that the BCE/CE usage is the less inclusive option since they are still using the Christian calendar numbers and forcing it on other nations. In 1993, the English-language expert Kenneth G. Wilson speculated a slippery slope scenario in his style guide that, "if we do end by casting aside the AD/BC convention, almost certainly some will argue that we ought to cast aside as well the conventional numbering system [that is, the method of numbering years] itself, given its Christian basis."

I'd really like for the numbering system to change, so I suppose that's an argument in favor of being annoying.