A refutation paragraph, found in argument essays, should start by introducing an opposing argument and acknowledging important points of the opposition. A writer's refutation paragraph should accept that certain parts of the opposition are valid, but show that the writer's claims are stronger.
According to Mesa Community College, a refutation paragraph or concession paragraph should have four sections. It should introduce the opposing argument, acknowledge valid parts of the opposition, make a counter or rebuttal to the opposing argument and introduce a conclusion.
Teaching Tolerance outlines a slightly different model. First, one should restate the argument being challenged. Second, one should refute the opposition's argument. Third, one should support his own argument with evidence. Finally, one should conclude a refutation with a comparison or restating of the main point.