Why should I be more "open-minded"?

An extremely common adage said by people who believe in the supernatural to skeptics is that they should be "more open-minded."

I have a question to them: Why, exactly?

And I'm asking this in all seriousness. I'm not debating what exactly they mean by "open-mindedness" (even though that's an interesting question in itself.) I'm going fully with theirdefinition of the concept. So, why exactly should I be more "open-minded"? What exactly would I benefit from being more "open-minded"?

They talk about "open-mindedness" like it were a positive, desirable thing, a good quality for a person, something that brings them something better. What, exactly?

In fact, these people usually don't actually have a clear and unambiguous definition of what "open-mindedness" means, but often it has something to do with accepting things as at least possible rather than rejecting them outright.

So my question is: Ok, if I start just accepting things as at least possible, how exactly do I benefit from that? What possible advantage or gain would I receive from doing that? How would my life become better?

Even the most hard-core believer ought to admit that at least some of those things will most probably be false explanations. So what exactly do I gain from "being open-minded" and considering them as plausible? The only thing I would end up doing is believing in falsities, sometimes even for my own detriment, and for what? What possible gain is there to be had from all this?

I find it interesting that the suggestion is always phrased as "you should be more open-minded" (or some variation of it.) Why should I?