because protestantism was popular in the US where there was separation of church and state. Its hard to fragment Catholicism when there is only one pope and one Vatican.
In Catholicism, the pope interpreted the Bible, but protestants protested the Catholic church for not following the Bible and not wanting the congregation to read it (back in medieval times). Once the Bible got into the hands of the average citizen, different people interpreted it differently. The differences in interpretation of the Bible caused different denominations. The catholic church was those who stayed under the leadership of the pope, so they didn't split.
Christianity fragmented many times.
The Great Schism is recorded around the First Millenium.
Eastern and Latin Rite Churches were identified and went their separate ways.
The Latin Rite became known as the Roman Catholic Church.
Followers of Jesus' teachings were first called Christians about 45 AD in Antioch. (Acts 11)
Protestantism branched from Catholicism. Protestantism basically derived from a search of an accurate interpretation of the Bible. Even today, new interpretations are being devised. As new interpretations form, new protestant denominations form. However, Catholicism is almost absolutely satisfied with its interpretations, doctrines and traditions; its consistent. Even if a catholic was to disagree with a doctrine of Catholicism, he would probably be considered protestant on the spot. That's what Protestantism is- a deviation from Catholicism.
Sorry, but you used the wrong term. Four major Protestant Church organizations exist: Greek Orthodox Catholic withdrew from dominance of the Roman Universal Catholic Church in about 1073 AD after many centuries of dispute. Martin Luther, a Catholic priest disagreed with the organization about the availability of the Holy Bible for the common man and a few other lesser items. He refused to back down, thus the Lutheran Church was formed and became the State Church of Germany in the early 1500'Rd's. John Calvin, another Catholic Priest and French had words and expressions of differences with the Roman Universal Catholic Church so withdrew a large congregation from her dominance forming the Switzerland Presbyterian Church. John Knox lead a group of Presbyterians, leading to the adoption of Scotland as their state church. This also was in the mid 1500'Rd's. Later 1500 or early 1600 AD Henry VIII wanted the church to grant him a divorce so he could marry an new lady, making her queen of England. The Roman Universal Catholic Church refused, Henry withdrew the nation from under the church forming a new State Church, the Church of England.
These are your Protestant churches, one dominated by the Roman Catholic. Three major true Christian churches emerged from the time of Christ on into today. These true Christians were called many names during their centuries of struggle again a persecuting state supported Catholic church as well as the four Protestant churches mentioned. The dominant name surrounding these three true Christian church groups was Ana-Baptist, not to be treated as if in respect. It was a slanderous name at the time. The Roman Catholic had adapted a policy of infant baptism, leading to that also bringing into membership of the church, leading into that being the sign of salvation---all coming from the Catholic themselves, not from Jesus nor his followers. The True Christians would not accept this form of baptismal interpretation when converts crossed over to the True Christians. So they had to be as saved individuals baptized as the True Christians followed Jesus.
Denominational association came much later and is associated more with the evangelical and fundamentalist than with the Protestant. The Protestant remained much organized and practice as did the Catholics, modifying where their original differences lie. Highly organized structure of a hierarchy. They did have splitting but are not inclined toward a denomination type structure. Episcopalians, Methodist and others are this type of example.
Many new voices were heard in the 1800'Rd's especially vocal during this period. Mormons, Jehovah Witness, Pentecostal, and many lesser known denominational types. Not so much break aways but more followers of ministers who held strong convictions about the interpretation of usually a small section of Scripture. This following of individuals has always been frowned upon by the more orthodox believers. Of this type of church we have maybe thirty sizable denominations at best, and perhaps hundreds of the cult and sect type with people confusing them with the denominations.
Now to answer your base question--Why did some church groups split and the Catholic did not. Freedom. The Catholic are a very dominating organization putting great pressure upon any opposition. The others, even the Protestant are more tolerant to opinions, so when groups disagree they were free to go off on their own. That is really a short coming of men rather than the doctrine preached by the individual churches.
Why did Protestantism fragment into a thousand denominations, whereas Catholicism did
