In an argument, some people will appeal to their own intuition as evidence that they're right and you're wrong. Unscientific? Yes. Patronizing? Yes. Always wrong? No. Sometimes intuition beats science.
Intuition: Fast, opaque, unreliable, context-dependent.
Science: Slow, transparent, reliable, context-free.
Intuitions are fast. Formalizing a hypothesis, constructing a theory, and gathering evidence, is a serious amount of work. Intuitions are rough but ready.
Intuitions are opaque. You think or even know you're right, but you have to introspect to find out why. It's believe first and ask questions later. Science works in reverse. You ask questions first, and only believe after you've got thorough answers. This makes science much better for resolving differences of opinion, since all the evidence is on the table, rather than being strewn across the uncollective subconscious.
Intuitions are unreliable. The fact that people have seriously incompatible intuitions should make us question our trust in intuition. If we are to trust our intuitions, we at least need good reasons why intuitions are reliable for us but not others. Similarly, we've all been sure of something that turned out to be wrong. Why were we wrong? How do we know we're right now? Without a way to evaluate intuitions, we either have to turn to science for answers, or admit that our beliefs are based on raw arrogance.
Intuitions are context-dependent. We routinely use intuitions successfully in situations untested in any laboratory. Business is impossible without a good sense of intuition. Intuition can't be practically reduced to a set of formulas you can follow for guaranteed success, no matter what the blurb on a self-help book says. Socializing is also impossible without intuition, as the hapless nerd aptly demonstrates applying science to social situations. This is not to say that context-dependent situations can't be informed by science, but that one's intuition takes the particulars of each situation into account and makes the final call.
Conversely, people often treat context-free situations as if they're context-dependent. Suppose your intuition tells you that the spooky sound coming from grandma's attic has got to be a ghost. The problem here is that the laws of physics apply in all contexts. Whatever you believe, has to be reconciled with what we know about fundamental forces. You heard it? You saw it? You saw the lamp it knocked over? This means the "immaterial" ghost is interacting with the material world, so physics apply to it. We must be able to detect one. Hell, let's capture one. In such an argument, the nonfictionally challenged X-File fan will actually try to inject context into a context-free situation. "My mama has never lied about anything..." In contrast to nerds, most people are weak in systemizing thinking. While a nerd may overly systemize when it comes to context-dependent situations, many people under-systemize when it comes to context-free situations well understood with the scientific method. This makes them vulnerable to believing in the supernatural and quackery. Often incapable of seeing any situation as context-free, they're eager to buy into the idea that truth is relative, oblivious - due to their lack of systemizing thinking - to the philosophical gravity that that position entails.