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.
Though slavery became the symbol over which the Civil War was fought after Lincoln's Emancipation Proclamation, prior to that, the grounds for war were not so much slavery as that the North fought to preserve the Union of the entire country while the South fought to preserve a way of life.
The South was very much an agricultural entity. The culture revolved around agrarian lifestyle or the maintaining of cultivated land. Huge plantation owners had acres of land to cultivate and maintain without enough laborers to maintain it. While the North had a much higher population twice the size of the south, its culture revolved around a more mechanized lifestyle. Over 90% of all industries of all types in the entire country existed in the North as did most of the railroad system. The only way the South could maintain the large plantations and exist as a mainly agriculturally sustained economy was to maintain slave use. To do that, they must win the Civil War.
In short, the South wanted to win the Civil War to maintain their way of life. The only way they knew to maintain the huge plantations without having the population and mechanization that the North had, was to utilize slave labor.