Seriously dude? I think you are being deliberately obtuse. But Ill play along for one of the examples, pink unicorns are not responsible for high Tc superconductors.
The first piece of evidence is biological, many species have been categorized and studied and no unicorn has even been scientifically observed. This is suggestive because large mammals are not easy to hide, thus this is evidence that unicorns likely do not exist. Furthermore, there is evidence that if unicorns did exist they would not be pink. Most mammals are not pink, and no horses are pink. If unicorns did exist then they would presumably be related to horses and thus also not be pink. Being pink could hardly be considered an advantageous trait so even in the unlikely case that unicorns did exist the fact that they would be pink would be very unlikely. Its pretty clear that there is copious amounts of evidence that pink unicorns do not exist (its still possible, but not at all probable). Even if they do exist, we then need to consider their effect on high Tc superconductors. In a broad sense no mammal on Earth has even been shown to be responsible for basic microscopic phenomenon. In fact, you may need to adopt some sort of top down causality where the macroscopic influences the microscopic - something that is common in biology but notably absent in physics. More specifically, the answer to low Tc superconductors comes from a unique and specific interaction between the lattice and the electrons. Though this description does not entirely work for high Tc superconductors, it is suggestive that the way to describe high Tc superconductors is also using novel interactions between the lattice and electrons (and not large mammals that have not yet been found).
All this is evidence. Its not absolutely conclusive, but no evidence ever is (in science). It may seem just like 'common sense' because it is basic evidence that we all take for granted, but it remains evidence nonetheless. And all this evidence is what we consciously or subconsciously use when we dismiss a claim that pink unicorns are the cause of high Tc superconductors.
The orbiting teapot is the example I like to use. Its often claimed that we don't assume a teapot is orbiting Mars simply because it is ridiculous and there is no evidence for it. But why is it ridiculous? Because there is evidence against it. We know what tea is, we know what a teapot is and we know who makes teapots. We know what it takes to put one in orbit and we know the history of mankind's (aka, tea drinker's) space exploration. This is all evidence against a teapot orbiting mars. If we didnt have this evidence, I would have to say there is a 50/50 chance of a teapot orbiting mars.