These three indisputable points are why Internet and other evangelical atheists are so boring. (When they aren’t being dicks.)
Just as religious faith is much more complex and sophisticated than some loud atheists like to pretend, atheism itself is usually much more sophisticated than people running around the Internet shouting that they can “prove” God isn’t real.
More thoughtful atheists (like me, lol) know perfectly well that proof one way or the other isn’t possible, and that that standard types of empirical evidence used in the physical sciences can’t shed light on the question.
For me (and many others), atheism is simply a lack of belief driven by a lack of indirect, cumulative evidence or personal experience. We know perfectly well that we cannot make any positive claims, so we don’t.
I suppose many people would call that sort of atheist an agnostic, and by popular definition, that may well be the correct word.
But philosophically speaking, the difference between lack of belief and lack of knowledge is rather important. Technically speaking in a philosophical sense, I lack belief in any god, so I define myself as an atheist, while understanding that for many people, that word is going to cause problems. They think I’m advancing a claim that I know perfectly well is philosophically impossible.