"10,000 people can't keep a secret!"

I can't remember the details of this discussion, but it went something like this:

Mr. A claims that the government wanted to test the effects of an atomic explosion on soldiers, so 10,000 (it was probably closer to 1,000) soldiers were transported into the desert to witness an atomic test.

Mr. B says "That wasn't a conspiracy, because it's impossible for 10,000 soldiers to keep a secret!"

Of course, this assumes the soldiers were told "Hey, guys, this is a conspiracy! We're going to tell the public that this is just a military drill, but we're actually going to test a new science fiction weapon on you."

Of course, one could speculate that Mr. B is just an idiot who really believes what he's saying. But for the sake of this question, let's say he's a propagandist who's deliberately making up an invalid argument.

Also, U.S. troops have probably witnessed more than one atomic blast, and I don't know what they were told in each specific instance. Again, this is a hypothetical example where the soldiers were NOT told they were being used as guinea pigs.

What kind of fallacy would this qualify as?

You say you can't remember the details, so was Mr A supposed to have said that it was a conspiracy to begin with? Otherwise I don't understand why the response would be that it isn't.

Then you appear to make an assumption that to be a conspiracy the subjects would need to be told it's a conspiracy. I don't understand how you arrive at this, nor who the conspiracy is against (as the conspiracy was never actually introduced, just rebutted), is it the soldiers or the public? I assume you mean the public but it would impact the soldiers not the public.

Calling Mr B an idiot appears to be poisoning the well, with a presupposition that he's wrong, when (if the conspiracy is supposedly against the public) he's got a point. Even if he was wrong, that doesn't mean it's a logical fallacy; not every wrong opinion is a logical fallacy.

The validity of the argument is predicated on human behaviour, not logic, and the higher the number of people involved in something secret (I really don't like the term conspiracy, the military and government don't have an obligation to declare what they're doing and doing so would be detrimental to the majority of their operations) the higher the chance of someone revealimg details to someone they shouldn't.

I don't know why you close with "again" and then provide details not previously mentioned. It might help if you clarified who the conspiracy was supposed to be against, though I'm not sure there's anything which would amount to that here. You might argue that "a secret plan which causes harm" would apply but then pretty much every military operation would be a conspiracy, where in reality it's simply chain of command and need to know.

Let's break this down into a simple argument:

Mr. A: "The government wanted to test the effects of an atomic explosion on soldiers, so X number of soldiers were transported into the desert to witness an atomic test."

Mr. B: "That wasn't a conspiracy, because it's impossible for X number soldiers to keep a secret!"

Several problems with this response:

1) Mr. B is making an unjustified claim using hyperbole (that it is "impossible").
2) Mr. B has committed a non-sequitur because keeping a secret isn't a necessary condition for a conspiracy to have taken place (we know about actual conspiracies because people involved did NOT keep secrets).
3) Mr. B just appears to be a poor communicator who does not know how to properly address conspiratorial claims.

Mr B. should have asked/replied:

1) What is your evidence that X number of soldiers were transported into the desert to witness an atomic test?
2) Many military personnel have witnessed atomic tests. What is your evidence that the point of this was to "test the effects of an atomic explosion on soldiers" rather than something much less nefarious?
3) Assuming the goal was to "test the effects of an atomic explosion on soldiers," how do you know these soldiers did not volunteer for this after being warned of the risks?
4) We know humans are bad at keeping secrets. Given this, it is far more likely that this event never happened as you described than X number of people involved keeping this a secret for so long.
5) If this is true and you have all this evidence, why don't you seek justice for these soldiers and take this case up with the proper authorities and legal channels, rather than posting them on Internet conspiracy forums along side claims of the government being run by lizard people and claims that Sandy Hook shooting never really happened?