First of all, we need to note that we cannot know for sure why so many whites supported the institution of slavery. There were no opinion polls or other ways to scientifically determine what attitudes people held. Therefore, historians have to make educated guesses.
Historians tend to make two arguments in this regard. First, they say that many of the Southerners who did not own slaves aspired to do so someday. This is similar to why people today who are not rich do not call for socialism. People today do not want to tear down the rich because they hope to be rich someday. Similarly, poorer whites in the South hoped to be rich enough to own slaves and did not hate the institution itself.
Second, historians say that slavery was good for the self-esteem of the poorer Southerners. Southern whites who were poor could still feel good about themselves because of slavery. They could know that, no matter how poor and degraded they were, they were white and that made them better than the slaves. This led them to want to keep slavery.