I think that statement is a bit strong. I have run into two kinds of atheists: True non-believers who just don't care what anyone else believes because they see that belief as inconsequential, and militant atheists who work hard to try to stop everyone from believing in God using everything from mockery to lawsuits.
The only explanation I have for the latter is that they really do believe in God, but are just trying to deny his Sovereignty over everything. Otherwise, they'd just look on believers like I would look on someone who uses horoscopes to make life decisions. They are a curiosity. I would think they have an inexplicable quirk, but we all do, so meh.
But, when the militant atheist makes all manner of effort to mock and to attack the beliefs of others, it must be because his professed, but unreal, nonbelief is being convicted by the Spirit, and so he feels the need to fight back, rather than submit to the authority of God.
Just my theory. However, I just realized that there would be an interesting corollary! If the militism with which he is responding is, in turn, a response to the Spirit convicting him, then militant atheists must be those whom God is trying to call, as opposed to true non-believers whom God is making no effort to reach!
I should change how I react to militant atheism. From now on, my response to militant atheism will be to throw a little Good News at their wall and see if any of it sticks. If God is indeed doing a Paul-job on them, my role would be to assist!
Nice job, Spirit, slappin' me upside the head with that one!