The basic reason why the South wanted to win in the American Civil War was so that they could govern themselves. They did not like being in a country that was, they felt, dominated by the North. They felt that the Northern states were dedicated to taking away their right to govern themselves.
The South tended to couch this issue in terms of states’ rights. They argued that states were sovereign and had the right to go against laws made by the federal government if they felt those laws were unconstitutional. However, their desire for states’ rights was not simply an issue of constitutional law and political ideology. Instead, much of what they wanted was the ability to continue to have slaves. The main reason why they feared being in a country that was dominated by the North was that they were afraid that slavery would be abolished.
The South wanted to win, then, because they wanted to govern themselves. However, much of their reason for wanting to govern themselves, free from federal control, was the fact that they wanted to maintain the system of slavery.