Of course we want to promote healthy skeptical attitudes ("healthy" being a key word here, but that's another post) in the general public. Skepticism is a critical part of the scientific mindset, and a properly skeptical outlook allows one to - essentially - not waste time and energy believing statements that aren't likely to be true.
But the application of that skeptical mindset can lead to more problems than it solves, especially when it comes to science communication. When does a debate become an argument? When it gets personal; when it shifts from discussing the relative merits or demerits of a particular position to the rightness or wrongness of what one believes. Once that shift happens, we haven't hit the iceberg yet...but it's hard to turn that ship around. If we're actually trying to educate, persuade, or inform, we're basically done.
Here's the problem: skepticism isn't a measure of the truthfulness of a statement, but its believability. It's perfectly acceptable to say "I don't believe that statement, but that doesn't make you wrong." Go ahead, try it out, it won't hurt. Statements can be 100% absolutely true but not able to be believed because of lack of evidence, and we all have different thresholds.
This shifts the discussion from things that a person might hold near and dear to their heart - and thus will righteously defend - back to the realm of the abstract. In this case, the nature of evidentiary standards.
In short, a skeptical person ought to be known having a high bar for believing statements, but it's nothing personal, and they won't hold it against you.