I have to agree with e-martin. While it does exist, a reason behind its existance does not. Essentially, all one can do is define their own reasoning behind why it exists (given it is, most likely, different for everyone).
That said, I believe that snobbery is simply another example of personal likes and dislikes. For many, snobbery comes from the fact that they tend to dislike those different from themselves. By deeming someone beneath them, a person can tend to be snobbish toward the other person. Many times this is the result of differences seen in Socioeconomic Status (SES).
The fact that many Americans, for example, share the same culture does not alleviate the fact that they are dissimilar on different levels.