I notice that you use a non-supernatural event for your example.
It IS more unreasonable for you to say you saw a ghost than to say you saw your shadow. Shadows are something we all see, we all experience, we can all go create a shadow if we want to. Seeing a ghost is, at best, speculation regarding an unexplained event.
Perhaps you are misunderstanding me. I am not denying that people experience unexplained things. I am saying that I don't accept their supernatural explanations for those events. If someone sees a light moving oddly in the sky and claims they saw an alien craft, I'm not going to believe that is the case, whether I find them trustworthy or not. I'll believe they saw something, but I won't accept the UFO explanation they have assigned to what they saw.
There are often non-supernatural explanations for things which, on first glance, may appear to be supernatural in origin. I think it is entirely reasonable to find it easier to believe something based on observable, repeatable events than something another person tells you which you cannot observe yourself.
When it comes to science which one either doesn't understand or cannot observe any aspects of, it's a different story.
Yes, those of us who have read much history at all KNOW that there were many supernatural explanations for poorly understood natural phenomenon of a particular era. But I used the shadow example because it IS something that is entirely common and that most people have experienced. But now, what if I came in and told you I just saw my shadow. And you look out and see that it is heavily overcast and beginning to rain. Now what would you think? Would you still believe I had seen my shadow? And, if I in fact had seen it, how would I prove that to you. Or would you assume that I had seen something else? Or misunderstood what I saw?
The point being that there are or can be components of our existence that we cannot explain with science and cannot prove to anybody. How do I prove to you that I dreamed last night? Or what I dreamed? And if I dreamed something that coincidentally then did happen, is it coincidence? Or some kind of paranormal event? How would we know?
You can keep an open mind to all possibilities without having to accept anybody's explanation for anything. It is rejecting the possibilities that slows the progress of our learning; not the embracing of them.
Again, using the example of a shadow just doesn't make sense. It would be better for you to say you DIDN'T see your shadow when you should; that would mesh more closely with supernatural claims. If you tell me you stood in front of a light but didn't cast a shadow it would be something that didn't make sense and I would find it hard to believe. Further, since I can easily repeat the process and see that standing in front of a light causes a shadow, I have good reason to dismiss your claims, especially if you then make some unsubstantiated claim like your lack of a shadow was caused by ghostly intervention.
While rejecting possibilities may be bad, accepting possibilities without any evidence is just as bad. Skepticism is perfectly healthy.
Skepticism is a resistance to belief based on reason, experience, or prejudice. It is a difference animal than disbelief or denial, but not the same thing as embracing a concept in hopes that it is true.
Perhaps it is reasonable to be skeptical of something based on one or two accounts of something happening when the vast reservoir of experience contradicts those one or two accounts.
But using an example I used earlier:
You do not believe that pink elephants exist.
But if one, then another, then another, then dozens of people came into the place where you are, and each one reported that he or she had seen a pink elephant outside, would you continue to believe that pink elephants do not exist?
. . . or. . . .
would you more likely think that
a) this was an organized practical joke?. . .or
b) they were seeing something that they interpreted as a pink elephant. . .or
c) they saw a pink elephant?
And sooner or later, would you be sufficiently curious to go see for yourself?
So you look outside. No pink elephant. But the people inside are absolutely convinced that they saw one and you are persuaded that it was no practical joke or organized effort and these people did not even know each other and had not communicated in any way with each other.
Now what do you believe?
If it was only one or two 'nuts' reporting paranormal experiences, it is reasonable to be skeptical or even a non believer. But when you have hundreds or thousands of people, none who know each other or have communicated with each other in any way, reporting paranormal experiences, and many of these are absolutely normal people with no motive or stimulus to encourage any unusual behavior or reactions, now what is it more normal to believe?
If scientists had shrugged their shoulders and said this or that didn't exist or wasn't true purely because nobody had ever 'proved it' or verified its existance, we wouldn't have a fraction of the scientific knowledge that we now have.
Bacteria and viruses existed for a very long time before anybody was able to verify their existance.
In my opinion, to assume that something isn't so because it has not yet been conclusively verified is to shut oneself off from 99+% of all that there is to know.