I suppose that a theist could just make the opposite claim.
Perhaps, but it would be far more problematic for him. How does one claim to believe in a deity
for no particular reason?
I don't think that can work very well, if at all. Theism is supposed to exist as a function of a belief, which by its turn involves
some conception of deity.
To say that one believes in that
just because is... exceedingly odd IMO.
One reason to participate in a forum like this is to get different perspectives from other intelligent folks who disagree with us. Or we could just go into our respective corners and not talk to each other. If the goal is to engage theists in conversation, then arguing over who has the burden of proof probably isn't a winning strategy.
Ah, but why is the burden of proof a subject at all? As a reaction against social and religious pressure for (usually empty) belief or at least the semblance of belief in deities.
The true question isn't whether it is a bad argument, but rather why an argument for atheism is at all demanded.