...sigh...
Only if you have neither.
Incorrect. You can have pleasure without pain: consider that a child when firstborn smiles when they see their mother. They are experiencing pleasure before they've ever experienced pain. It's conceivable to think of a logically possible world where pain does not exist but pleasure does without logical contradiction as well, so your dualism is false.
Likewise, theism can exist if atheism didn't -- consider that there's no logical contradiction to think of a world in which 100% of the people existing believed in gods. There is no contradiction there, so again, your dualism has no logical force.
If theism didn't exist then indeed there would be no word for "atheism" but people would still be what we call atheists -- they would lack belief in gods, since they wouldn't think about or know what a "god" is in the first place.
Your dualisms are not correct. No need to "sigh," we're working this out cordially
And if you have (or don't have) such justification, both atheism and theism remain. Do you believe that theism is unjustified?
If yes, then theism should be gone.
If no, then atheism should be gone.
Both of these statements are untrue.
None of those statements made sense, considering it was backwards. Theism has the onus of proof, not atheism (unless it's strong atheism, which I'm not proposing here). The person claiming the existence of something has the burden of evidence.
There either
is justification for theism or there is
not.
If there
is, then theists
are justified and atheists are
not justified upon cognizing this hypothetical justification.
If there is
not, then theists are
not justified whereas atheists
are justified by withholding belief in it (since it's unjustified).
So, your dualisms are false and we are back to the original question: Is there a valid justification for theistic belief?
Edit: Also I think I mistook what you said for "Do you believe atheism is justified?" So anyway, in regard to your statement that one of them should be gone, that's not true -- it would be true if everyone were epistemically responsible and believed only that which they had justification for but that isn't the case. People believe in unjustified things all the time as Atomist pointed out. So, no, a lack of justification wouldn't mean that a
belief would be "gone." But we can establish whether said belief is rational or not. Theism is irrational if not justified.