The sky is the blue (or black, or cloudy) vault that comprises the visual limit of the eye. Things that appear to be above you such that that vault appears as their backdrop are said to be "in the sky." The tops of skyscrapers appear to be "in the sky" as do birds and airplanes.
But an airplane taking off or a bird flitting from a low branch to the ground is moving through the air, but is not in the sky. A fly ball in baseball may appear to be sky-high momentarily, but eventually comes to earth. It's all about perspective and point of view.
They are most certainly not the same, and while it is true that air is more colloquial than evince, that's a relatively small part of the difference.
Far more important is the idea of intentionality. If I air an opinion, it's because I want you to know what I think, and I've consciously written or said something to achieve that goal. I can evince an opinion, on the other hand, entirely by accident in any number of additional ways — through the work I do, the people I associate with, the web sites I visit, or through discourse apparently unrelated to the opinion in question.
The Oxford Dictionary definition of evince, for example, is simply to "reveal or indicate the presence of a quality or feeling." Who or what does the revealing is irrelevant.
To cite an example from today's news: In response to a journalist's question about China's trade practices, Donald Trump said the Chinese have broken every agreement, sought every unfair advantage, and and done whatever they can get away with. He doesn't blame them for that, but he'll put an end to it if he's elected.
Mr. Trump aired an opinion about trade policy. At the same time, he evinced an opinion about morality and proper behavior — the idea that it's not blameworthy to break agreements and do whatever you can get away with.
Finally, it should be noted that neither air nor evince is entirely right for the general case of "to make one's opinion known." To give, express, state, or share an opinion would all be more appropriate.
As noted by others, evince has a legalistic feel, while air implies a particular kind of discussion — involving both informality and a minimum level of disagreement. Grievances are on par with opinions in the word's Oxford Dictionary definition, and insubstantiality comes from the word itself.
Given that the context mentions hot issues and diverse perspectives, air may well be the best choice in this particular case. But generally speaking, you don't air an opinion if you're sure you're right, if you don't expect any pushback, or if you're more powerful than your listeners. You and your spouse might air opinions on household spending. But your doctor wouldn't air her opinion on how long you have to live, and judges don't air opinions in court.
Best Answer
For me, "disappeared without a trace" and "vanished into thin air" mean the same thing.
"Disappeared without trace" seems ungrammatical in American English. I don't know about other brands. Could it be like "He's in hospital"?
"All the chocolates vanished away in no time at all" seems not idiomatic to me because of away. Lewis Carroll, however, used it in The Hunting of the Snark:
Whether this was just for the rhyme (and, therefore, poetic license) or was (and maybe still is) idiomatic British English, I don't know.