In philosophy appeals to intuition, and intuition pumps, are commonplace. For example we might show that a claim has implications that are so absurd that we can’t accept them, and thus we reject the claim, even though it may be only our intuitions that tell us they are impossible. More concretely, epistemologists often show a definition of knowledge to be in error by showing it implies that some beliefs, which we intuitively know not to be knowledge, are knowledge.
As useful as they may be, however, intuitions can be as harmful as they are helpful. For example, the fact that the earth goes around the sun may contradict our intuitions (or at least it contradicts the intuitions of some people), but that is not a good reason to reject it. Likewise, some philosophers have argued that we intuitively just know the mind to be separate from the body, or that zombies (in the philosophical sense) could exist. Again, this is bad reasoning.
To avoid such pitfalls some would argue that we should reject intuitions altogether. It is true that science could proceed without intuitions, but this is not the case in philosophy. For example, the claim that the mind controls behavior, and that conscious minds necessarily posses a first person perspective, are our intuitions about the mind, they are not facts that we can back up with evidence. Discarding all of our intuitions would result in the inability to do philosophical work in many areas; an acceptable solution must allow us to tackle philosophical problems and eliminate the possibly problematic applications of intuitions.
Fortunately the answer is simple. Intuitions are to be used only when laying out the requirements that a good definition of a concept must meet or the properties a natural feature of the world which corresponds to the concept most posses. Intuitions are used incorrectly when we reject a conclusion about reality, and not our concepts, because of them. We should expect our intuitions to track what our concepts mean fairly well, since they are both products of our mind, but there is no good reason to expect our intuitions to match reality.
So showing that a certain definition of knowledge labels some beliefs as knowledge that we intuitively know not to be knowledge is a good refutation of that definition, because here we are exploring the concept of knowledge. On the other hand, one cannot reject a proposed reasoning strategy by showing that the information it provides isn’t always what we call knowledge. The only good reason to reject a reasoning strategy is by showing that it is leads to excessive errors or is surpassed by some other strategy. Of course we could conclude that the reasoning strategy doesn’t align with our concept of knowledge by appeals to intuition, but this is somewhat of a wasted effort, since it doesn’t give us reason to reject it (maybe what we think of as knowledge isn’t the best way to reason).