Here are three key points to make when debating the existence of God (which are particularly important for atheists to remember).
1. Defining God
First, in asking ‘Does God exist?’ it would be good to get some clarity about which God we are talking about.
I shall assume we are talking about a God that is omniscient, omnipotent, and perfectly good. For that is a standard definition. For example, the Christian philosopher William Lane Craig defines God as a ‘maximally great being’ – which he says requires that God be morally perfect. Richard Swinburne similarly characterizes God as ‘a person who is omnipotent, omniscient, and perfectly good’.
It suffices to establish atheism, then – given these philosophers' characterizations/definitions of theism – that we show beyond reasonable doubt that there's no being that is omniscient, omnipotent, and perfectly good.
Suppose at the end of a debate over the existence of God it's suggested that we have not shown that God does not exist because we have not refuted every variety of god hypothesis – we haven't ruled out Zeus, or Odin, or the Manichean gods. Nor have we ruled out an all-powerful but morally indifferent God, or a morally perfect but less than omnipotent God.
In response to that, the atheist can point out: for pretty much everyone in the room, the existence of these other gods is simply not an issue. Those in the room who say they believe in God and indeed worship God do not believe in the existence of an omnipotent but morally indifferent being. They too are atheists when it comes to a God like that.
If the atheist can succeed in establishing beyond reasonable doubt that an omnipotent, omniscient, perfectly good god – a god actually worthy of our worship – does not exist, then, against theistic opponents like Craig and Swinburne, they can rightly consider that a win.
2. Beware the dodgy ‘cumulative case’
Second, here's a simple logical point sometimes overlooked in such debates. Often, those arguing for the existence of God offer a number of arguments. For example, they may offer first a cosmological argument for there being a first cause and necessary being, second a teleological argument for there being a designing intelligence, third an argument for this being being a person, fourth an argument for this being being morally perfect, and so on.
But now notice that all but one of these arguments could be sound and yet still the case for their God might more or less entirely collapse. Let's suppose they do have a sound cosmological argument for a first cause, a necessary being. Let's suppose they do have a good argument for there being a designing intelligence.
Still, it will suffice to refute their case for their God if we can show that they have no good case for supposing that this necessary being, designing intelligence, and so on, is also perfectly good. For if we can show that, then there still remain all sorts of gods on the table of which theirs is just one candidate. They've given us no reason yet to prefer their candidate over any of these various other candidate gods, such as morally indifferent God, say, or an evil God. But then their case fails.
3. ‘But still, we are now pretty close to showing God exists'
Finally, if we can establish beyond reasonable doubt that whether or not there's an omnipotent, omniscient being, a designing intelligence, and so on, there's ample evidence to establish that this being is not perfectly good – and thus ample evidence that this being is not your God – the God you worship – it won't do to say:
‘But look – at least we have established there is a necessary being, a first cause, a cosmic person, and a designing intelligence. So you have to admit we are nearly there when it comes to establishing the existence of our God. Indeed, our cosmological and fine-tuning and other arguments for God can be set against your argument against the existence of our God, leaving us, as it were, all square. While you have, we admit, a good argument against the existence of our God, we have several good arguments for! So you see, the arguments cancel out. This debate has ended in a draw!’
The truth is you will have got nowhere near establishing the existence of your God.
The situation is akin to claiming that because the police have shown that the murderer lives in this village, they're close to showing that Bert, who lives in the village, is guilty. Actually, they're clearly nowhere near showing that. And if there's good evidence Bert didn't do it (he's got a good alibi, let's suppose) – well then the police case against him is utterly demolished.
The theist's claim that they're at least near to showing God exists above is equally ludicrous, and only fails to seem so in their eyes because they mentally airbrush out all the other candidates (like a policeman mentally airbrushing out everyone else in the village but Bert in order to convince himself the case for/against Bert's guilt is balanced).