Is the Catholic church 2000 years old?

Catholic apologists compare their "2000-year-old" church to upstart Protestant denominations. I've discussed that before, but I'll expand on that:

1. Suppose a young couple buys a Fixer Upper. At the time it's all they can afford on their meager income. As their income rises, they remodel the house. As their income continues to rise, they make additions on either side. Finally, they demolish the original house, preserve the additions, and build a new house in-between the flankers. Is the final house the same house as the original house?

There's a kind of historical continuity in play. But no part of the original house exists. It's been replaced, part by part. And not even by the same kinds of parts, but different kinds of parts. It's unrecognizable compared to the Fixer Upper. So mere historical continuity doesn't make it the same house or even similar to the original house. 

Moreover, even if some of the original parts were preserved, it's undergone so much change that it's equivocal to say it's the same house. It's the same in some respects but not the same in key respects. 

2. There are different ways a faith-tradition might be new. On the one hand, it might have new doctrines, new interpretations. On the other hand, it might be a new combination of old doctrines and old interpretations. It might recombine them in different ways.

3. To some extent, Protestant theology was new. It emerged in the 16C. However, it didn't pop in out of the blue. In many respects it had theological antecedents. And Protestants claim it's older than Catholicism because it represents a restoration of biblical theology, from which Catholicism deviated. 

However, the Catholic church under Pope Francis, or even under Pope Benedict XVI or Pope John-Paul II, is a different church than it was under Leo XIII or Pius IX. The Catholic church under Pope Innocent X and Pope Clement IX is a different church from the medieval church. By condemning Jansenism, they anathematized the Augustinian tradition. What held an honorable place in Catholicism prior to Calvinism became intolerable after Calvinism. Catholic theology is reactionary. 

One could give many other examples. There really is no such thing as "the Roman Catholic Church" because it keeps reinventing itself. Just as the Protestant movement emerged in the 16C, Catholicism reemerges in different mutations throughout the course of church history. 

4. Catholic apologists save face by distinguishing between two different kinds of change: 

i) In the case of inconsistent changes, those are extraneous to what's essential to Catholicism. Those were never dogmatic, infallible, irreformable, de fide teachings. 

ii) Other changes represent the development of doctrine. They are said to be consistent with dogma.   

But while that may be persuasive to conservative Catholics, it cuts no ice when debating with Protestants, since we don't grant their distinctions. These are ad hoc distinctions superimposed on Catholicism despite the evidence. While Catholics naturally assume a Catholic viewpoint, they can't reasonably expect or demand that Protestants share their viewpoint. So comparing their "2000-year-old" church to the Protestant faith begs the question. When we look at the history of Catholicism, we don't see a 2000-year-old church. Rather, we witness a dialectical succession of ideas. 

Like any historical process, you can retrace current developments to antecedent conditions and causes. That holds true for Catholicism and evangelicalism alike. But that doesn't mean the house standing on the same property as the Fixer Upper is the same house.