“For some believers, they would love nothing more than to convert nonbelievers. The opposite goes for atheists as well."

The first part of that paragraph is true. The second part is false. There are a few, like Ben Cain, who will independently offer up articles explaining the logic behind atheism, trying desperately to keep the arguments on an intellectual level. But the vast majority of arguments are initiated and pushed by theists. Atheists, in general, could not give a rat’s patootie whether someone else wants to believe in God or not. It extremely rare to find an atheist saying "You need to stop believing in God".

When we argue back it is because we just don’t like being told that we are wrong using superfluous arguments and logical fallacies, nor do we appreciate being called immoral, and we chafe at the conventional wisdom that views us as weirdos with suppressed horns on our heads. And we are vehemently opposed to theists using their beliefs to try and force their religious values, mores, laws, and rituals on us.

But when we argue our points, the arguments are based on logic, reason, and evidence. Theists on the other hand make grand, platitudinal, almost rhetorical claims about things with zero evidence, and base their whole argument on the idea of “prove what I just said is not true.” The false burden of having to prove a negative is the main foundation of the theist argument.