Un-falsifiable means it can't be falsified, but falsifiable means it can be falsified.
That's not a definition of either word. It's a definition of "un," which we see is the equivalent of "not." And there is no indication of what falsifiable means. It's like writing that antidisestablishmentarianism means opposed to disestablishmentarianism. Not a very useful definition, like Kramer's definition of quone:
Also, I don't see what point you think @SkepticThinker confirmed, or how she confirmed it. Was it, "Missing Links everywhere, but oops, it was falsifiable"? Or was it that, "there's lists and lists of falsified stuff from the scientific community"? Or maybe, "if I provided you with said evidence, would you believe your eyes, or your heart, or your mind - if you even knew the nature of your mind, or your heart and eyes. You do not know, and the sciences do not know, but currently it's all guesswork; jab it, poke it, cut it."
The person claimed to want, "falsifiable evidence," which means: evidence that can be falsified.
I posted earlier that this phrase is a category error, like claiming that a law has been fulfilled*. Evidence can't be falsified. It can only be observed and interpreted. Only statements can be falsified, not objects or processes. Evidence can falsify a statement, but cannot itself be falsified. If the theory of evolution is ever falsified, what will be falsified is the narrative of the theory, not the evidence used to form the theory, nor the falsifying find, all of which is still truly evidence, now needing a narrative to account for. Thus falsifying evidence makes sense, but falsifiable evidence does not.
*[Laws can be enacted, obeyed, modified, flouted, etc., but they cannot be fulfilled (or smelled or painted, for example). Promises and dreams can be fulfilled, but not laws, just as evidence can be discovered, interpreted, etc., but not falsified. That's what's meant by category error. I'm sure you recognize where the claim that laws can and have been fulfilled comes from.]
If you make an unfalsifiable claim, then you are making a claim that cannot be demonstrated to be false/wrong. It's something of a useless claim that doesn't get us anywhere. If you make a falsifiable claim, you are making a claim that can be demonstrated to be false\wrong. These claims are actually useful ones that can get us somewhere.
I agree with this, but would quibble with the wording here and in "Falsifiability is the capacity for some proposition, statement, theory or hypothesis to be proven wrong." Falsifiability as I understand means that if a statement is incorrect, then a certain kind of evidence can show that to be the case if it exists and can be found. It isn't necessary that that evidence ever be found for the statement to be called falsifiable, just that one can conceive of evidence that if found would disprove (falsify) the statement. Evolution is falsifiable, but will never be falsified, because it is correct, thus falsifiability doesn't mean that the statement can be falsified. The statement might be correct.
Thus, both metaphysical statements and correct statements cannot be falsified, but for different reasons, and the former are called unfalsifiable while the latter are falsifiable even though not false. You can see my objection to the wording above. Evolution is falsifiable, but there is no 'capacity for it to be proven wrong' if it is correct.