As noted, in the late nineteenth century, the Catholic Church in the United States was doing quite well, despite existing in a mostly Protestant country in which Protestants were largely suspicious of Catholics. It was expanding, it was doing exciting new things, it seemed remarkably unified, and both laity and clergy were very active in works of charity. This contrasted with the way things were at the time in many European countries, where the Catholic Church, despite being more entrenched, was often struggling, and perhaps most of all in France. So what made the difference?
One possible interpretation you could have, which has some initial plausibility, is this: the big difference between the two cases is that in Europe, the Church was integrated into the government, while in America there was separation of Church and state, so that much of what the American Church could accomplish was entirely by popular support, and the laity had considerably more influence on the course of things in the United States than they had elsewhere. In addition, the separation guaranteed that the Church never became identified with one particular regime, the way that the Church in France had become associated with the monarchists and therefore ran into problems when France -- yet again -- became a republic. In 1892, Pope Leo XIII encouraged Catholics to participate in the life of the French republic, and it became inevitable that French Catholic intellectuals would look to the American example for ideas about how to do this.
One of the more successful examples of the generally successful American Church was the Missionary Society of Saint Paul the Apostle, usually know as the Paulist Fathers. The Paulists had been founded by Isaac Thomas Hecker and a few others with the purpose of engaging in Catholic evangelizing in the United States, and they had experimented, often successfully, with all sorts of ways for reaching their fellow Americans. This is not particularly surprising, and probably has more to do with American culture than separation of church and state, because Americans at the time were experimenting with all sorts of different things -- new ways to use print media, new kinds of communities, new kinds of voluntary associations, new fads pertaining to health, society, religion, you name it. Very likely none of it could be replicated with the same success elsewhere, regardless of the hopes of certain European progressive Catholics. But there was no doubt that the Paulists were very successful in the American context.
The result of this was that a biography of Hecker was translated into French within a few years, and read avidly by French progressives interested in the question of being Catholic in a republic; Europeans more generally were eager to hear about Paulist ideas and projects and constantly put forward their own projects for change as inspired by the American model; and more conservative Catholics began to be very wary of this reformist project that seemed to be spouting new and untried ideas on a regular basis and advocated a major overhaul of how the Church related to the society around it. It was inevitable that people would start complaining to Pope Leo XIII, and they did.
Leo XIII was one of those people who have conservative principles but progressive sympathies. He had engaged in a number of reform projects himself, and had actually been quite impressed with many of the things being accomplished by the Church in America. But he was also convinced that there was a genuine problem here; what was being called the American approach to things was in some places radically upending entirely healthy Catholic culture, and the principles did seem to be found in the French translation of that biography of Hecker. So out of this came Testem benevolentiae nostrae, the condemnation of Americanism.
Written to James Cardinal Gibbons, who was bishop of Baltimore, the chief American see, and notably walks a very careful line to avoid accusing anyone in particular (including Fr. Hecker himself) of actually affirming the heresy. The essential idea underlying the heresy, Leo XIII wrote, "is that, in order to more easily attract those who differ from her, the Church should shape her teachings more in accord with the spirit of the age", and the spirit of the age was interpreted as especially exemplified in a focus on action and practice over doctrine and prayer. To tone down or omit parts of Catholic doctrine simply in order to make the whole seem more palatable to non-Catholics was absolutely unacceptable. Likewise, the approach led to downplaying the value of spiritual direction and of consecrated life in a misguided belief that this empowers individuals. For the same reason it would often deprecate virtues and practices associated specifically with prayer in comparison with civic and social virtues.
Given the history, it's sometimes said that Americanism was, despite the name, more a European heresy than an American one -- that is essentially how the American bishops responded to the Pope's letter. And there's certainly something to that. There probably was, however, an Americanist strain in some corners of the Catholic Church in America; the Europeans weren't manufacturing it out of thin air, although they attributed many things to the American approach that were probably more wishful thinking than genuinely American. But Leo is very careful in the letter to forestall any temptation to suggest that being American was in any way the problem, so the heresy needs to be distinguished from other things that you might call 'Americanism':
From the foregoing it is manifest, beloved son, that we are not able to give approval to those views which, in their collective sense, are called by some “Americanism.” But if by this name are to be understood certain endowments of mind which belong to the American people, just as other characteristics belong to various other nations, and if, moreover, by it is designated your political condition and the laws and customs by which you are governed, there is no reason to take exception to the name. But if this is to be so understood that the doctrines which have been adverted to above are not only indicated, but exalted, there can be no manner of doubt that our venerable brethren, the bishops of America, would be the first to repudiate and condemn it as being most injurious to themselves and to their country.
One of the things I have long noted is a tendency to try to use the name to stuff anything one doesn't like about American life under the label of the heresy; but this must be fully avoided.
