If all Buddhists ultimately desire to attain Nirvana, then isn't that a contradiction if they can't attain it as long as they have desire? I am confused.

Don't be confused by the word "desire" used to explain the causes of suffering with the "desire" used to describe one's wish or will. An example of the former is our greed, some examples of the latter are birthday wishes and our ambition. Obsession about satisfying desire ultimately leads to all kinds of suffering, while fulfilling a wish keeps one's mind focused and directional. Once we make a wish, we may not be as obsessive as satisfying our desire to fulfill the wish. The "desire" to attain Nirvana is an aspiration to all Buddhists who have to be mindful of all conditions that may obstruct them to attain it, including their own "obsessive desire" to attain it.