The scenario outlined above most closely relates to the Tu Quoque (you too) fallacy. It's essentially saying, I can ignore your criticisms because you haven't come up with a solution. More broadly it is a Red Herring, and even more broadly, a Non-sequitur. (Sadly, this is all "good debate form" if you're only interested in winning.)
Hi, A search for a certain kind of fallacy led me and a friend to the Skeptic's Field Guide, and so I though I'd ask if you have any input on our question: You mention Burden of Solution as a fallacy in which "[t]he Advocate denigrates a suggested solution to a problem but fails to propose a viable alternative."
My friend had been wondering if the opposite could also be considered a fallacy: invalidating all criticism of a suggested solution because the one offering the criticisms can't offer a better one... or rather, "Oh, yeah? Well, I'd like to see YOU come up with something better", in response to valid criticisms of a solution. It seems like such a position would be fallacious (or at least bad debate form), but neither of us can find a name or definition for it. Can you offer any advice?
This is a tough one in terms of getting the balance between the Burden of Solution and valid criticism right. Arguably, it's not a critic's job to find solutions. They're a critic. A good critic, however, offers constructive criticism and tries to find ways forward.
The Tu Quoque aspect of this is how the advocate maneuvers the conversation. They don't dismiss the criticism per se, but change the focus from the criticism to the lack of a solution from the critic. Hence the Red Herring. The critic in this case should say, "Let's stay on topic. I never claimed to have an alternative solution for you. It's not my job to find the solution. I'm drawing attention to the specific issues I have with your proposed actions."
If both parties are acting in good faith and are genuine seekers of a solution, the critic should not only point out flaws, they should try to offer a solution or at least admit they don't have one either. And on receiving criticism, the advocate would not dismiss it out of hand because the critic didn't offer any solutions. Of course, this would require rational and disinterested discourse... a common experience of the world at large and the internet in particular.