Science has its limits. It's very materialistic. You can't test things you know nothing about, because you either can't come up with a working test, or you can't even detect what you are trying to test.
The tiger example is a very good analogy and shows where "science" has failed in the past. There have been reports in the past of strange animals, and the experts would say it was folklore or mistaken identification. Then someone finally traps or kills one.. and look at that, we now have the gorilla! That was in 1901! Prior to 1847, the gorilla was the 'yeti' of Central Africa. It was dismissed as a "silly native legend". Now we are finding new plants and animals all the time.
Science is an important thing, but you have to accept that it has its limits. Plus the attitude of many scientists are that of skeptics, so they wont even accept paranormal events like the sighting of ghosts. But if 100 people see the same phenomena over and over, you can't dismiss it just because "science" can't test for it. Science just hasn't come up with a working hypothesis, or a way to test for it.
The same thing happens when they try and test for physic phenomena. The tests often break the phenomena, but that's a failing of the testing procedure and not the phenomena itself.
You really have to open your horizons a little and stop holding so tightly to our tiny view of reality. There are more things that we don't know, than we do, and science is always rewriting the facts.
Astronomy is a good example. It's purely observational for the most part. When I was a kid many of the "facts" in the astronomy books are different from the "facts" now. We learn new things, and former theories are shown to be wrong, and new ones are thought up. And every now and then you have the refreshing "We don't know" about something.
So history has proven that you can't discount things just because you can't hold them in your hands, or test them using the scientific method. If you don't understand the mechanisms behind something you can't test it.
People just don't want to admit that we don't really understand reality and we don't know everything. What you can see and test is only a tiny fraction of reality.
