A common argument in support of god’s existence is, and has always been, the supposed occurrence of miracles; from Zeus sending down bolts of lightning to Yahweh parting the Red Sea; from the miracles and resurrection of Jesus, to on-camera feats of Sathya Sai Baba. It’s hard to think of a single religion or cult that does not depend in some way on miracle stories.
When debunking miracle arguments for the existence of god (keep in mind that not all miracle arguments are meant to prove god’s existence), it’s important to remember that almost all of these arguments are composed of two parts. First, that a miracle actually occurred (as in, a suspension of the laws of nature), and secondly, that this is proof of god’s existence, since there would supposedly be no other way to explain such a thing. It is therefore important to maintain the distinction between these two parts, and to debunk each in its turn. Flip-flopping back and forth between these two parts, or claiming that there are no parts to begin with, are well known religious tactics that you should try not to fall for.
Let’s start with the first part, the part that talks about the laws of nature being broken. A good place to begin is to point out that even the suggestion that the laws of nature were broken is self refuting. There are two reasons for this: First, if a thing has actually occurred, then that thing, to the extent of its occurrence, is natural. It might be rare, or may have even been a singularity, but if the thing actually happened, then it happened within nature. When a thing that had never been observed before breaks a known law of nature, we call it a discovery, which we then use to amend and adjust that law of nature, not declare the thing as a miracle. And science is actually full of such discoveries. Secondly, claiming that an unnatural/supernatural occurrence has taken place is loaded with the prerequisite of knowing everything there could possibly be to know about nature and the laws the govern it – otherwise, how could you know that a thing is outside of nature?
By claiming that something is supernatural, a person is either admitting they don’t understand how it happened naturally, or that the thing didn’t actually happen (at least not in the way they think it did).
David Hume had famously said that if you think you are witnessing a miracle, you must weigh the probability of the laws of nature being broken against the probability of your being under a misapprehension or delusion. This also means that if you only heard about the miracle from someone else, you must add the possibility of the person telling you about the miracle being under a misapprehension or lying about it. And if the story about the miracle is thousands of years old, and conveyed through many discrepant translations of translations, of stories from a time when people understood close to nothing about the natural world, the probabilities must be adjusted further.
Another useful way of looking at the miracle issue is by considering what it is you are seeing (or not seeing) when skilled illusionists, say, like Penn and Teller are performing. It should quickly come into focus that regardless of how convincing it may seem, and despite the fact that you have no idea how what you saw (or thought you saw) just happened, you do realize you did not just witness a miracle. As counterintuitive as it may seem, to claim to have seen something you cannot explain, says more about your own subjective experience than it does about what objectively happened – a fact that all illusionists (and unfortunately many religious leaders) have long learned to exploit.
As for the second part of this argument, the part about the miracle (even if it were to be real) proving that god exists, this is a simple Non Sequitur. There just isn’t enough substance to logically bridge the gap between a magical event and the existence of a specific deity (Yahweh, Allah, Vishnu, etc). One of the easiest ways to reveal this disconnect is to ask the followers of one religion if a miracle story from another religion proves the existence of that other religion’s deity – and vice versa. Nothing exposes this non sequitur faster than the arbitrary and biased manner in which some miracle stories are cherry picked while others are dismissed.
In conclusion, miracle arguments for the existence of god are almost always dependant on simple logical fallacies:
1. “The laws of nature have been broken.” = Begging the question – how the speaker knows everything there is to know about the laws of nature.
2. “It must have been a miracle, how else could you explain what happened?” = an Argument From Ignorance.
3. “This miracle proves that Yahweh/Allah/Vishnu exists.” = Cherry Picking + Non Sequitur.

There is one more important factor to keep in mind when debating miracle arguments for the existence of god, however. Though miracle arguments are, logically speaking, extremely weak, they do tend to be extremely convincing for those who advance them. It’s therefore important to make a clear distinction between how someone subjectively feels about what they experienced, and what objectively happened. As much as people don’t want to hear that they might have been confused, or deceived, they will often cut out of the debate altogether if you tell them that they didn’t even experience anything. I find it useful to empathise here, and to tell my counterpart that I do realize they experienced something powerful and profound, and that so have I at various times; but the gap between subjective feelings and objective reality can only be bridged by reason and evidence. And until it is, the only logical thing to do is to suspend judgement. It might be deflating for many people to realize this but the “you simply had to have been there” element is just another way of describing a subjective experience; and subjective experiences cannot support objective claims.