There's plenty of great commentary here about why Christianity is divided up into different sects, but I think you're primarily interested in the narcissism of small differences. (https://en.m.wikipedia.org/wiki/Narcissism_of_small_differences)
Basically, if you've read about Dr. Suess' Starbellied Sneeches, you get the idea. Human brains are exceptional pattern recognition machines, and when a society is so homogenously Christian then those small differences become the cleavages along which identities form. That leads to things like Catholic / Christian divisions and the formation of the best joke in The Guardian history:
Once I saw this guy on a bridge about to jump. I said, "Don't do it!" He said, "Nobody loves me." I said, "God loves you. Do you believe in God?"
He said, "Yes." I said, "Are you a Christian or a Jew?" He said, "A Christian." I said, "Me, too! Protestant or Catholic?" He said, "Protestant." I said, "Me, too! What franchise?" He said, "Baptist." I said, "Me, too! Northern Baptist or Southern Baptist?" He said, "Northern Baptist." I said, "Me, too! Northern Conservative Baptist or Northern Liberal Baptist?"
He said, "Northern Conservative Baptist." I said, "Me, too! Northern Conservative Baptist Great Lakes Region, or Northern Conservative Baptist Eastern Region?" He said, "Northern Conservative Baptist Great Lakes Region." I said, "Me, too!"
Northern Conservative†Baptist Great Lakes Region Council of 1879, or Northern Conservative Baptist Great Lakes Region Council of 1912?" He said, "Northern Conservative Baptist Great Lakes Region Council of 1912." I said, "Die, heretic!" And I pushed him over.
https://www.theguardian.com/stage/2005/sep/29/comedy.religion
With all due respect, this is not reflective of the protestant revival movement in the US in the 1800s. The second awakening was absolutely a bunch of rival interpretations of the word claiming they were right b/c (insert reason here).
I probably should have been more specific in my original reply but when we're taking about US "Catholics aren't Christians" that's 100 percent the origin of the trope. I can't speak to the Irish version but I'd challenge anyone about it in the US. That's why we needed an Ecumenism movement in the first place after all.