I think the arguments are stacked either way:

It is just as rational to believe 'God exists' as it is to believe 'God does not exist'.

But the million dollar question: What do I mean by God?

I think that contradictory states of affairs cannot exist. Hence, if Gods nature is contradictory then God cannot exist. If we 'discover' Gods nature is contradictory then we have a choice, however:
1) We can conclude that God does not exist
2) We can revise our conception of God

I choose to revise my conception of God in the face of contradiction and hence I can get clearer on the nature of the possible Gods that could exist...

That gives us a range of possibilities as to what Gods nature is like...

Then...

Whether we believe in one of those Gods or not...

Is a matter of faith.

A matter of faith.

Where reason leaves off faith soars

It requires just as much faith to say 'God exists' as it does to say 'God does not exist'. Either way is a matter of faith...

A conception of the relationship between reason and faith that I really struggle with is the conception that where reason delivers a contradiction faith can persist IN SPITE OF reason. I struggle with that. I really think that God (if he exists) gave us reason for a reason... Such a reason may be (for example)... To better contemplate his nature.