I'm not really sure how much more basic it can be made than the difference between "I do not believe there is a God" and "I do believe there is not a God". There's a fundamental difference between asserting something and failing to assert something else. It's not actually binary.
I fully grasp the difference.
"I do not believe there is a god", can mean one of two things. It does not imply the agnostic position, because the "moron" atheist can say this line and it would be true as well.
There is no reason to say "I do not believe there is a god" without giving it the context of "I do not believe or disbelieve in a god", that would be the more proper way to express the opinion and make a person's position far clearer with just a couple more words, saving pages of debate. This is hardly relevant to my point, though.
I would say the position that should be argued against is "I believe god has been proven false", not "I disbelieve in god". Why? Well, the average person proves my point for me, all but the complete deniers of reality itself.
Now, it is my opinion that you are almost certainly not a billionaire, etc. However, I won't assert as fact that you are not, because I don't know that.
I am either a billionaire or not. There are only three beliefs to take - that I am one, that I am not one, or that you can't know, so you take neither stance. You are mixing up the belief in the
probability and the belief in the
actuality. But the belief in the probability is asserting a belief that the probability is true and accurate, that you disbelieve the idea it is false. This will apply to every assumption and belief you have. If someone disbelieves I am a billionaire, then they have asserted they believe the fact that I am not, not that the fact is proven, by the very nature of disbelief. Your position should exclude you from ever disbelieving anything, unless you believe absolute truths can be proven.