...cannot pretend it did not happen just to satisfy the doubters.
Just so you know, I'm not wanting to doubt or believe. But the neutral position is to not believe until sufficient evidence is presented.
Once you have experienced a supernatural phenomenon
What constitues sufficient evidence for a "supernatural phenomenon"? Some people, due to superstitious backgrounds, will immediately ascribe a supernatural explanation to a strange unexplained or unexplainable event.
The skeptic or scientist would rather investigate the hell out of such an event to see if there's a reasonable explanation first and only assign a label once it is found. And ultimately, if the event has no clear explanation, it remains unexplained. There may be a hypothesis but no dogmatic assertion that X absolutely caused Y.