There are at least two reasons why African American vernacular is looked down upon in American society today.
The first of these reasons is racism. African Americans have long been the group within the United States that has the lowest status. Anything that is associated with that group exclusively has therefore typically been looked down upon. This has been true of various forms of music, for example. It is true with language as well.
The second reason for this is that African American vernacular is not the language of commerce and formal situations. Languages or dialects that are typically only used in informal situations will tend to be looked down upon. This happens, for example, with “Pidgin” or Hawaiian Creole English in Hawaii. Since this language is not used in formal situations it is looked down upon. It is the same way with African American vernacular, which is why there was such a huge controversy over the idea of using “Ebonics” in the formal setting of public schools.
African American vernacular, then, is looked down upon both because of its association with African Americans and for the fact that it is not the dialect that is used in formal situations.