When faced with the lack of evidence of God's existence, one of the favorite retorts of religious people is, "Well, you can't prove that God doesn't exist."
I've been prone to argue back, the burden of proof is on the person making a claim that something exists. Or, it is impossible to prove a negative.
But these are rather simplistic responses. I've come to feel that a more nuanced reply should be, "Hell, yes, I can prove that God doesn't exist."
Here's how it can be done.
Get some specifics from the God-believer. What are the characteristics of this God you consider to exist? What does this God do? Where does this God reside? How does someone know this God is present to them?
After all, there are lots of supposed gods. Immaterial and material. Personal and impersonal. Eternal and timebound.
It is indeed possible for me to prove that something does not exist if the entity is more than a vague abstraction. I can prove there isn't a full grown giraffe in my kitchen by looking everywhere an animal that size could hide without being seen.
Which, actually, is nowhere.
If God is described with enough specificity, proof of God's non-existence becomes feasible. For example, if God is believed to regularly overturn the laws of nature, then regular evidence of these miracles should be evident. If such doesn't exist, then it can inferred that this sort of God doesn't either.
It also is important to remind the God-believer that 100% proof isn't possible. We're talking about probabilities when it comes to something being true, or untrue.
After all, tomorrow it is possible the sun will disappear, all dogs will start talking in perfect English, or gravity will reverse itself. The fact that these events have a very low probability of happening makes us confident they won't exist tomorrow.
But someone could argue, "Well, you can't prove this." Of course not. We have to consider the reasons for believing they might occur, then judge how likely it is one of the events will happen.
It is fallacious to say that because something either exists or doesn't exist, there's a 50-50 chance of each. Lots of religious believers think this way, though. So reminding them about probabilities introduces a healthy dose of reality into a debate over whether God exists.
How sure are you that God exists? 90% sure? 20%? 1%? By contrast, how sure are you that electricity exists? 99.9%? What is the basis for whatever percentage of confidence you have?
Again, it isn't possible to say with 100% confidence that anything is true, or isn't true; exists, or doesn't exist.
We always can think of reasons to doubt any statement.
I could, for instance, resort to a "Matrix" sort of argument no matter what your claim is: Sure, it seems that electricity is real. But what if we actually are part of an alien computer simulation where the programmer has added an electromagnetism feature to the virtual world?
So considering specifics and probabilities go a long way toward proving that something either exists or doesn't exist.
At some point common sense rules. If there is no demonstrable evidence that something with characteristics X,Y,Z exists outside of a human mind that believes it is real, we say "it doesn't exist." Ditto if the evidence is so shaky and minimal, the probability of the thing's existence is exceedingly low.
Check out "You Can Prove a Negative."
Let's sum up. If "you can't prove a negative" means you can't prove beyond reasonable doubt that certain things don't exist, then the claim is just false. We prove the nonexistence of things on a regular basis. If, on the other hand, "you can't prove a negative" means you cannot prove beyond all possible doubt that something does not exist, well, that may, arguably, be true.
But so what? That point is irrelevant so far as defending beliefs in supernatural entities against the charge that science and/or reason have established beyond reasonable doubt that they don't exist.
Here's the Stephen Hales paper by the same name that inspired the above-linked Psychology Today piece.
The very nature of an inductive argument is to make a conclusion probable, but not certain, given the truth of the premises. That [is] just what an inductive argument is. We’d better not dismiss induction because we’re not getting certainty out of it, though. Why do you think that the sun will rise tomorrow? Not because of observation (you can’t observe the future!), but because that’s what it has always done in the past.
Why do you think that if you turn on the kitchen tap that water will come out instead of chocolate? Why do you think you’ll find your house where you last left it? Why do you think lunch will be nourishing instead of deadly? Again, because that’s the way things have always been in the past. In other words, we use inferences — induction — from past experiences in every aspect of our lives.
...So why is it that people insist that you can’t prove a negative? I think it is the result of two things. (1) an acknowledgement that induction is not bulletproof, airtight, and infallible, and (2) a desperate desire to keep believing whatever one believes, even if all the evidence is against it.
That’s why people keep believing in alien abductions, even when flying saucers always turn out to be weather balloons, stealth jets, comets, or too much alcohol. You can’t prove a negative! You can’t prove that there are no alien abductions!
Meaning: your argument against aliens is inductive, therefore not incontrovertible, and since I want to believe in aliens, I’m going to dismiss the argument no matter how overwhelming the evidence against aliens, and no matter how vanishingly small the chance of extraterrestrial abduction.