Nihilism is a strawman that is easy to attack. Prior to Nihilism the strawman of our tradition was Skepticism. But when we look back at Skepticism of Sextus Empiricus we find that it is actually a very interesting approach to things seemingly modeled on Buddhism. But the images of it that are attacked almost by everyone are nothing like genuine Skepticism at all.
Quora answer: Is nihilism a self-defeating philosophy?
What is odd is that Nihilism has taken the place of Skepticism as the strawman that everyone attacks. But nihilism it is argued by Nietzsche and Heidegger is precisely the point of view of the Western tradition itself. In other words, when we attack nihilism we are attacking our fundamental viewpoint which produces nihilistic extreme opposites in almost every sphere of life. But those nihilistic extreme opposites come to the same thing in the end, so there is a loss of the ability to make distinctions, and a loss of meaning.
So your question can be construed as asking if the Nihilism of the Western tradition, its dualism is self-defeating. And the answer to that is probably yes. However, that self defeat is a long drawn out war of attrition between the various nihilistic opposites that are produced by the worldview, like mind/body for instance from Descartes.
How we get out of this self defeating situation, this kind of kakatopia, hell on earth, is by making non-nihilistic distinctions. But the problem is that those distinctions that would find the middle ground between the extremes are almost impossible to find because the nihilistic opposites have become disconnected from each other, and the middle ground has become lost to our sight. So the real question is how do we stop defeating ourselves?