There is a certain type of mind that delights in paradoxes, to the extent that even after an explanation has been clearly produced, the person will continue to insist there is a paradox.
Naming things paradoxes attracts this sort of individual, so it's a kind of marketing ploy for an idea: it won't just get it talked about, it'll get it talked about forever, because each generation of paradox-mongers will take it up anew and discuss it and analyze it and do absolutely anything except acknowledge that the specific flaw in the reasoning that leads to the appearance of an impossible conclusion being true was exposed generations ago.
For example, consider the supposed paradox of the evening star and morning star, which I will first state in the a way that makes it clear there is no paradox, then restate in the traditional way.
"The Evening Star is Venus seen in the evening sky."
"The Morning Star is Venus seen in the morning sky."
"Transitivity implies therefore that the Evening Star is the Morning Star, since Venus seen in the evening sky is Venus seen in the morning sky."
This is obviously stupid: no one would make this claim. The traditional formulation actually depends on a falsehood, or at least on radically incomplete statements:
"The Evening Star is the planet Venus."
"The Morning Star is the planet Venus."
"Transitivity implies therefore that the Evening Star is the Morning Star, since the planet Venus is the planet Venus."
At this point, you can spend millions of words explaining why the statements identifying lights in the sky viewed at a particular time of day with a ball of rock orbiting the sun are problematic. It will be pointless: paradox-mongers will simply not let their nice toy be demolished.
Most traditional paradoxes have straightforward resolutions (frequently involving inserting a knowing subject into them, like the person who observes Venus) but none of them will ever be "solved" because of this purely psychological resistance to the possibility of their solution on the part of a very vocal sub-population.
One useful trick is to never let a paradox be stated in the traditional way. The first step in any discussion should be to restate the paradoxical situation as completely as possible, usually by introducing the perspective of particular individuals, as I've done above. Traditional paradoxes almost all depend on very specific ways of stating them for their psychological effect, and breaking out of that ritual pattern of restatement often makes them look simply stupid. One can then ask what is missing in the ritual statement of the paradox that makes it not seem stupid.
In the case of the Potato Paradox, the restatements we've seen here, which introduce the ratio 1:99 as the way to think about the problem, is a good example of this. Since the answer is not intuitive, the correct way to introduce the problem is to make it intuitive, not to blurt out a non-intuitive answer and expect the now-confused listener to catch up. That's just bad pedagogy.