For me as an atheist it's not about choice either.If that's the case, then atheists need to stop telling me what it means to be agnostic!I definitely reject the binary choice idea. What passes for my belief system is based around not making a choice!
In fact choosing to believe is an impossibility for me.
I couldn't believe it even if I wanted to.
Believing something requires me to be convinced.
I can not choose to ignore information I have, just as I can not choose to not be able to read anymore.
I can choose however to question information and test it to be true as best as I can.
Belief and disbelief is merely a necessary result from that.
I know that you see 3 states essentially.
To hold something as true, untrue or undetermined, right?
But only holding something true makes you a believer, can you agree to that?
Now if holding something untrue or indetermined does not make you a believer, what does that leave except an unbeliever?
In the case of the god claim, not being a theist just leaves being an atheist, as in not being convinced a god exists no matter if you are willing to keep testing the god hypothesis further or not.
I really don't understand where this notion cones from that being an atheist only means being convinced that no god exists as it literally just means not believing the positive claim.