I have recently been confronted by a person who, obviously being an angry militant atheist, said that "the Church has advocated the view that the Earth is flat, and killed thousands and thousands of people who argued that the Earth is not flat."
It sounds as though the flat Earth concept confused with the
geocentric model. I don't know if anyone was executed over the heliocentric model. Copernicus might have published his
De revolutionibus orbium coelestium at about the time of his death, but it was most likely published postmortem, all without any interaction with the always diabolical Latins and their evil Pope-king (sarcasm).
Most people are referring to Galileo's trouble with the Roman Inquisition, which condemned geocentrism as a heresy which is contrary to the Holy Scriptures. They were correct in that geocentrism contradicts the Biblical cosmology; that the Biblical texts are wrong on some scientific matters (for example, the sun "stopping" its movement across the firmament, although we have had other discussions of the relativity of the center of the universe, which in fact saves the Bible from this particular incrimination). At any rate, he was eventually condemned by the Latin church for his views and forced to recant and spend the remainder of his life under house arrest.
I don't know if his refusal to recant would have been met with execution. Perhaps someone else knows the answer to that and can provide an appropriate citation?
At any rate, the accusation that thousands upon thousands of people were executed by the Latin church over this issue is preposterous, and all the tangent reveals is that this person has a problem with Christianity and is looking for any excuse to dismiss it.
Also, these little tidbit from Wikipedia are very interesting:
On 15 February 1990, in a speech delivered at the Sapienza University of Rome, Cardinal Ratzinger (later to become Pope Benedict XVI) cited some current views on the Galileo affair as forming what he called "a symptomatic case that permits us to see how deep the self-doubt of the modern age, of science and technology goes today." Some of the views he cited were those of the philosopher Paul Feyerabend, whom he quoted as saying “The Church at the time of Galileo kept much more closely to reason than did Galileo himself, and she took into consideration the ethical and social consequences of Galileo's teaching too. Her verdict against Galileo was rational and just and the revision of this verdict can be justified only on the grounds of what is politically opportune.” The Cardinal did not clearly indicate whether he agreed or disagreed with Feyerabend's assertions. He did, however, say "It would be foolish to construct an impulsive apologetic on the basis of such views."
On 31 October 1992, Pope John Paul II expressed regret for how the Galileo affair was handled, and issued a declaration acknowledging the errors committed by the Catholic church tribunal that judged the scientific positions of Galileo Galilei, as the result of a study conducted by the Pontifical Council for Culture. In March 2008 the Vatican proposed to complete its rehabilitation of Galileo by erecting a statue of him inside the Vatican walls. In December of the same year, during events to mark the 400th anniversary of Galileo's earliest telescopic observations, Pope Benedict XVI praised his contributions to astronomy.