Why do minorities continue in society?

What does your question mean? Are you stating that there should be no minorities? Please be specific.

One could answer your question, as phrased:

Because we, as a society, do not advocate genocide; however I don't believe that is what you meant. Do you mean to ask, "Why do certain groups in the United States tend to resist assimilation?", and even that assumes that certain groups do, intentionally, make efforts to resist assimilation, and assumptions are not facts.