Why did some white Americans, especially in the deep South, react negatively towards the decision of Brown v. the Board of Education?

Because they didn't want their white kids going to the same school with other black kids. They had this negative stigma that black people were violent, dangerous, and would put their kids in harm way. Plus some white people, especially in the south were just pure racist and didn't like that black people were for the first time receiving preferential treatment.