The revolutionary leaders split over the direction of the new nation in the 1790s because of external events and because of differences in their views as to what an ideal country looked like. In essence, they were breaking into political parties because they no longer had the goal of independence to keep them unified.
As the new country was getting started, the leaders had to decide what they wanted the country to look like. They fell into two main categories on this issue. One group, that we now call Federalists, wanted the country to become industrialized and economically powerful. They felt that a strong national government was needed to help achieve this goal. They did not mind if the industrialization led to a degree of social and economic stratification. Finally, they were somewhat suspicious of democracy, feeling that the people as a whole did not know enough to rule themselves directly. This group is most closely associated with Alexander Hamilton. The second group, now known as the Democratic-Republicans, was led by Thomas Jefferson. This group wanted a country that was made up of small farmers. These farmers would all be independent and would all be equal to one another. This would make for a perfect democracy because everyone (or at least every white man) would be equal to every other.
These groups were further split by events overseas. Specifically, they were split by the French Revolution and by the war between France and Britain that followed. The Federalists were horrified by the French Revolution and felt that the more conservative British system of government was preferable to French-style democracy. The Democratic-Republicans approved of the French Revolution and saw the British system as a form of tyranny. The conflict between France and Britain forced these nascent parties to take sides, further splitting the revolutionary leaders.
Thus, we can see that the leaders of the Revolution later split with one another because they had divergent views as to what an ideal country would look like.
They were split because of their different beliefs and ideology. These were mainly between the Federalists and the Democrat-Republicans. While the Federalists wanted a stronger country in overall, the Democrat-Republicans wanted the people to have equal rights and for the country to exist under the leadership of democracy.
Revolutionary leaders during the 1790s began to disagree on how the government should run. They split into two parties, the federalists and the democrats. Federalists believed in a strong federal government compared to strong state governments. On the other hand, the democratic party believed in the opposite: more state rights and a decentralized government. They were run by different leaders, like Hamilton, who had different views and ideas.