The difference between showing a belief to be irrational and showing that God does not exist

On the top of 7, Plantinga distinguishes positive arguments for thinking God does not exist from showing belief in God to be irrational. I already addressed this issue in an earlier post, but there are some things that worry me. Given the present debate and the number of arguments in the theistic arsenal, it's not entirely clear that if atheists have responses to each argument, that belief in God becomes irrational. As I have noted before, two different philosophers can hold contradictory views and supply much evidence for them and both can still be rational in holding to their views. I develop this in depth in my dissertation. Given the power of the theistic arguments and disagreements over whether atheists have adequately responded to something like the kalam cosmological argument, I don't think we are in the land of rationally or irrationality when the discussion occurs among talented philosophers. I think the most brilliant theist and the most brilliant atheist can be rational in holding to their views. (I won't go into the reasons.) But suppose the atheist has shown that belief in God is irrational (in my last post I noted problems interpreting this claim). Are they then licenced to conclude that God doesn't exist. If so, then the burden is on the theist. In fact, the atheist need not give arguments for thinking God does not exist since if they show that each of our arguments fail and the burden of proof is on us, they have won.
My question is whether this is right. How can we show that both bear a burden and thus the atheist must show God doesn't exist instead of playing defense and attacking theistic arguments? (The preceding may be nonsense, but the question is still important.)