In linguistics, there is a blurry line between when two languages are really dialects and when two dialects are really languages. If I understand you but think you talk differently from the way I do, then we are probably speaking two different dialects of the same language. However, there are two facts that make this distinction less clear. So the very idea that two people can speak the same dialect is an abstract concept to begin with. Secondly, languages do not exist in a vacuum.
Language is part of culture, and as such gets highly politicized.
It turns out, for example, that Swedish and Norwegian are probably two dialects of the same language. Tell this to a Swede or a Norwegian, however, and you might get hurt, because neither Sweden nor Norway will admit to speaking a language even vaguely connected to that of their closest rival. On the other side is the example of Mandarin and Cantonese Chinese. In its attempt to appear as unified as possible, China claims that these mutually unintelligible languages are really dialects of the same language. This politicization is at the heart of the Ebonics debate.