Certain people will often eschew a certain premise of an argument because it only relies on intuition. Intuition is faulty, they say, and so it cannot be trusted. They try to rid themselves of believing things simply based upon intuition. Now, intuition is faulty and can be open to defeaters, but that doesn’t entail that intuition should never be trusted. However, the person who denies intuitions runs into a deeper problem.
Edmund Gettier is famous for his paper that shows that knowledge is much more complex than originally thought (this seems to be the simplest way of explaining it without taking a certain stand on the solution). But what exactly does Gettier do in the paper? It’s this: he wants us to intuitively believe certain things (say, that Smith doesn’t have knowledge about Brown’s whereabouts–see case 2). Hence, to agree with the Gettier counterexamples is to use one’s intuition. Therefore, to reject one’s intuition is to reject the Gettier counterexamples, and that seems problematic.