Take relativism, for example. Relativists deny the existence of absolutes. But, think about this claim for a moment. In the denial of absolutes, you have created an absolute, for you have claimed that there are absolutely no absolutes. In less, of course, you meant that there are only no absolutes in certain contexts, which makes even less sense.
Then, of course, there's nihilism. Nihilists deny the existence of values and our ability to communicate with one another. As for the first claim (the denial of the existence of values), I wonder what sort of value Nihilists assess nihilism as being, for they certainly seem to hold the value of the denial of values, and the value of the denial of our ability to communicate with one another. Then there is the second claim (the denial of our ability to communicate with one another). Nihilism is a belief commonly held and expressed by multiple individuals. I'm not sure how the first nihilist communicated their nihilism to the second, but they apparently did, proving nihilism to be false. If we weren't able to communicate with one another, then I would not be able to even know what nihilism is. Since I have heard of nihilism, nihilism proves itself to be false.
“The Promised Land always lies on the other side of a wilderness.”