Joe believes a god does exist.
John doesn't believe a god does exist.
Fact is there is lack of evidence for a god existing and lack of evidence for a god not existing because science has no stance either way.
So my question is if both have lack of evidence, isn't what is chosen to accept merely based on personal choice?
Atheists don't believe in God. That is not the same as believing that there is no God. To believe that there is no God, they would have to have
proof that God doesn't exist. To not believe that there is a God, they would have to
lack proof that there is a good. Let me reiterate: It is a matter of
having proof of existence vs. lacking proof of non-existence.
An axiom of logic says that you
can't prove a negative. So, it is illogical to assert that something doesn't exist. For example, you cannot prove that Santa Claus doesn't exist because you would have to prove that right now he doesn't exist, a minute from now he doesn't exist, he doesn't exist in California, he doesn't exist in Nevada, etc.
So, an atheist can claim to not believe in God without having the proof that God doesn't exist. This is because there is no proof that God does exist.
Atheists require proof before they believe.
There are an infinite number of things that you could believe in if you didn't require proof. Leprechauns, the tooth fairy, and even a made up cartoon character, like Fred Flintstone.
Surely you don't want to believe in absolutely everything?
Theists believe without proof.
But
atheists believe in other things without proof, too. For example, an atheist doesn't have proof that his wife isn't cheating on him. An atheist doesn't have proof that a car on the road will stop at a stop light and not run over him. If it wasn't for some level of belief, it would be very difficult for one to leave the safety of their home. Even then, they'd have to have some belief that someone would bring them food.
Belief could be strengthened by building trust by doing trustworthy things in the past. For example, cars have always stopped without running you over in the past, so they will likely stop in the future. What if they do run you over (accidents happen). To some, those are random events, and won't happen again. To others, such events cause them to lose faith.
Often it is better to trust someone until they give you reason for you not to trust them.