I appreciate the thorough criticism, but I don’t think it would be worthwhile for me to respond to each of your points here since each would lead to a separate debate. Instead, I’ll sketch further how I think the argument from incoherence can be applied to Catholicism and to Christianity in general.

Catholicism is bound to be incoherent because of what was often the political way the Church established its “universality,” by demonizing foreign viewpoints, symbols, holidays and so on, or by assimilating them. The assimilation of so many disparate cults and cultures, from Jewish monotheism to the Mystery cults and Roman polytheism, from Mithraism and Marcionism to the worship of goddesses and saints is bound to make for a tattered theological framework.

Indeed, early Christian theologians embraced the resulting incoherence as a sign of Christianity’s majesty. “It is certain because it is impossible,” said Tertullian, and Paul said, “For the wisdom of this world is foolishness in God’s sight.”

These are concessions that Christian theology isn’t going to be logically airtight, as far as “natural” beings can tell, because God transcends our comprehension. But this is also an excuse for Christian imperialism, for the arbitrariness of Christian doctrinal assimilations and of its pragmatic, Roman compromises.

I’d direct you, then, to the Incarnation and Trinity doctrines, and I’d note their incoherence. And I’d direct you to the clash between Christian myths and allegories, such as you find in the gospel narratives, and the abstraction of the Scholastic deity (the first cause, necessary being, etc, derived from Aristotelian naturalism). Finally, I’d direct you to the clash between Jesus’s counterculture and his ascetic repudiation of social conventions, on the one hand, and on the other the Christian institution’s wholesale betrayal of that subversive message, which was done for political reasons, to justify the Church’s wealth and power owing to its having inherited the Roman Empire.

You say the Catholic Church hasn’t modernized, but that’s quite false. Indeed, the Church modernized itself before modernity. Remember that modernity in Europe reached back to ancient Greco-Roman naturalism and secular humanism, which represented proto-modernity two and a half millennia before modernity, as it were. By trying to reconcile Christian theology with Plato and Aristotle, the Church sowed the seeds of its self-destruction, by presupposing rational standards and by injecting proto-naturalism into what would have to be myths for the Christian contents to serve a religious purpose.

The Scholastic abstractions, then, are modernizations. The systematicity of the Church hierarchy, derived from Roman imperial infrastructure, was another modernization, compared to the ragtag nature of the Jesus movement in the first century CE. Then there were the Second Vatican Council, and the embrace of Darwinism.

I think you’re confusing liberalism with modernism. The Church has largely retained its social conservatism, to its detriment in literate, developed societies. But liberalism isn’t the only facet of modernism. And the conservatism of the Catholic elites doesn’t reflect the liberalism of many lay Catholics, so that’s yet another bit of incoherence.