Why might the people of a country want to blame a minority group for most of the country's problems?

Because it's easy. For example, it is easy to blame minorities that they are stealing jobs from the majority. The problem with that is that if a person who does not have many social contacts nor that much of an education and can still get the job and do it correctly, then the problem is not that the minority got the job that they obviously deserve, but that the majority just wants an excuse for personal failures.