If such phenomena cannot be deomstrated to others, then it is perfectly reasonably for others not to believe it isn't it?
Yes, it's perfectly reasonable to reject the idea as demonstrable, not but as real. To demonstrate unreality is the cumbersome task of proving a negative. While it can be done, the circumstances must be exact or else the test becomes invalidated. There is a monumental difference between something that isn't demonstrable and something that isn't real. That would be like calling a mystery not real simply because it's a mystery.
Lets say that you are a sheep herder and every night you lose one sheep to an unknown cause. Although you have a mystery on your hands, you still feel the negative effects of it. Eventually you will be out of sheep and lose your livelihood. Therefore, it would be unreasonable to live your life as if your sheep were not disappearing simply because you cannot explain why. This is how atheists view unexplainable phenomenon. They say that because we cannot explain how we interact with it we shouldn't be concerned with it. We should treat concepts such as the soul and the afterlife as if they didn't exist until evidence turns up that explains the mystery. This is like living in denial of your sheep disappearing one by one because you lack the ability to explain it.