I mentioned before I thought this was related somewhat to the teaching “once a Catholic, always a Catholic”. This doesn’t, I think, just affect people in self-identification. I suspect it may also lead to people who have real problems with CC teachings to stay in the Church rather than leave.
First of all, if people are told that whatever they think or do they are still a Catholic in some sense, it seems logical to say “although I disagree about the CC teaching on contraception, I will remain here, because I am still part of the Catholic Church”.
And I also think there is kind of a gut reaction among many people. Having been taught their whole lives that Catholicism IS the Church, they have a hard time leaving that. If they accept that even unconsciously, they may come to the conclusion that some of her teachings are wrong - and of course it is true that the CC has never been a perfect institution, so may be able able to see the things they disagree with in this light.
Also, they probably find the argument that they are subjecting the Church to their reason as somewhat unconvincing. What is sometimes glossed over in that is even those who choose to submit their reason and will to the Church have done so because they believe that the Church is what it claims to be. No one advocates just taking the word of any institution or person that it is God’s direct messenger - lots of crazy people have claimed that. And when people do that, choose to be Catholic, they have subjected the content of Catholisism to their scrutiny. I think that how this fits together is something that could many times be better presented, because when some people claim that “real” Catholics never do it is clearly false.