We can identify at least two main beliefs or values that formed the foundation for Du Bois's rejection of Booker T. Washington.
First, we can see that Du Bois held a very strong pride in his race. He was reported to have said that he was glad that he had no "Anglo-Saxon" blood in him. (He did have some white blood, but not "Anglo-Saxon.") His pride in his race led him to be impatient with accommodationist teachings such as those of Washington.
Second, we can also see that Du Bois valued aggression and assertiveness. Growing up in the North, he had a much different background and upbringing than Washington did. This difference made Du Bois much more apt to be confrontational towards whites who subjugated African Americans. Therefore, he rejected Washington's idea of being patient and waiting for whites to recognize the value of African Americans.