The point here is that exposing a logical contradiction is just the beginning of a useful criticism. If the contradiction we point out is real, then we have essentially challenged the speaker to revise his or her views in one of several possible ways. A full, fair, critique, must take account of the various possible ways that this can be done. Suppose I believe that atheists are bad people, and that all my friends are good people. But Mr. Pheeper, my long-time friend, decides that he is an atheist.
All atheists are bad people.
These four statements are logically contradictory, because they jointly imply that Mr. Pheeper is both a good person and a bad person. Logic requires some sort of revision to my set of beliefs, but logic does not demand one particular revision. The point is that these are all possible solutions, each of which must be examined on their own merits. Most people find it difficult to identify contradictions in an explicit way, but it is important to learn to do so. Here is an explicit definition of a contradiction together with the proper method for identifying one.