The phrase, in and of itself, isn't inherently a fallacy, although it's usage is often suspect.
Well, fallacy is the subjective part. Name me a fallacy, I'll give you an example where it's incorrect and another where it's correct.
Let's take the 'slippery slope'. If we ban handguns, the next thing you know they'll be taking all guns! And then installing a dictatorship!
Now the thing is, the above is a 'slippery slope' if it's inaccurate - but the very same statement isn't a fallacy if it happens to be correct. That's where the debate lies.
If I said 'if we give the government to ban books they think are dangerous to security, in no time they'll be banning any book that's politically inconvenient for them'.
Is that a slippery slope? Maybe, maybe not - it might be right or wrong. But it fits the forum of the fallacy, if you think it's incorrect.
A reason I called 'if you ban x, only outlalws will have x' a fallacy is because it fools many people into thinking it completely addressed the issue of 'banning x' when it does the opposite, preventing consideration of the primary purpose of the ban - how many outlaws will not have x if it's banned?
The implication of the phrase - without saying it explicitly - is that every law-abiding citizen will no longer have 'x' but every criminal who has 'x' will continue to do so.
And that may or may not be the case.
Let's take an example - say handguns are banned. Two possibilites are, there's a significant reduction in criminals with handguns; or there is no reduction.
Which is the case? That saying offers exactly nothing to answer the question - while pretending to answer the policy with that implied 'there will be no reduction with criminals'.
But then you need to look at the question. The US is in a unique situation with its large number of guns in circulation, making any limit difficults. But when you look at the number of guns criminals get by stealing them, it's pretty clear there would be a reduction in the supply to steal, and therefore fewer for criminals, and raising the cost to them.
Since the saying does nothing to address the issue but make an insinuation without any basis, I'd call it a fallacy. Which is not to say it's always wrong, jjust as with others.
But you're skipping the second part of the argument. The first part - if we ban legal access to guns, it will also drive down access for illegal ownership of guns by restricting supply - is perfectly valid. But what about the second part: does the benefit of making it more difficult for criminals to obtain guns justify the cost of eliminating the right of law-abiding citizens to possess them? That all boils down to a matter of opinion. You clearly feel as though it's a small price to pay to help restrict the flow of guns into the hands of those who would use them to harm others (I'm guessing that you neither own nor have any interest in owning guns yourself).
Well, actually, I haven't stated an opinion on the issue - I did point out the need for someone who did to state what they think those costs are and why they weigh them.
The answer about my owning guns is yet another fallacy, the 'ad hominem', having no relevance to the issue - if I don't, 'ya, see, you can't discuss the issue you hate guns', if I do, 'well that didn't prove anything'. It's just an attempt to bring in an irrelevant issue to avoid having to defend a position.
I feel as though it is an unnecessary and overreaching restriction to place on law-abiding citizens for an assumed reduction in crime (I don't personally own guns, I have no interest in owning guns, I've never even fired a gun).
Making it even more clear why it's irrelevant if I own guns.
The benefit doesn't justify the cost in my opinion, and that's where there's a massive disconnect in the gun debate in this country right now. And it's a disconnect that is never going to change. The gun culture in our country goes down to our core, to the point where the founding fathers put an amendment about arms into the Bill of Rights before anything about due process or a trial by jury or freedom from cruel and unusual punishment. Fighting against guns is a losing battle on a national scale.
You oversimply the issue. First, the importance of the second amendment is first, no one says they're in order of importance (if the founding father did I haven't heard it). It's sometimes argued the first one is there for a reason that's a bit more credible but after that I don't see any support for it (the right not to have the government execute you without a proper trial is less important?)
Second, the importance of the second amendment is easily attributable to how at the time that was our only national defense as a weak new nation - pretty strong issue.
That's changed greatly - we're now about 20 times the military of the biggest potential 'rival' and citizens with firearms are not an important part of that.
Third - and this is the oversimplify part - opposing SOME gun rights is not "opposing guns".
This is the same rhetoric as saying that people who vote against a military program are 'against the military' or that opposing a war means you're 'for the other country'.
First of all, unless someone opposes all guns everywhere including the military, you can't just say they're 'fighting against guns'. You have to be more specific and accurate about their position. Second, your simplified version is more of that ad hominem - 'you support a specific measure therefore anyone who isn't totally against guns has to disagree with you'.
We're not really in much disagreement about the need for the discussion to discuss the costs of each option and why one is more important, but that hasn't happened a lot here.
You state a conclusion about the cost, but there's not much support. I haven't stated much opinion on the issue at this point. Just the fallacies being argued so far.