Actually, that’s too strong a statement. It would be more true to say that I, and many other atheists, do not believe that there is such a thing as a soul. We can’t say conclusively that there isn’t; it’s just that we haven’t seen convincing evidence for it yet, so we don’t believe it.
Incidentally, there are atheists who do believe in souls. The concept, after all, is not inextricably tied to belief in or worship of a god. It’s just that I’m not one of those atheists, so please don't think that I'm speaking for them in this post.
Now, when I say a soul, I’m talking about a magical, immaterial and potentially immortal component of consciousness/personality that can survive independently of a living brain and body. That’s the thing that I don’t believe exists.
The problem is that the word “soul” has acquired a lot of cultural baggage, and a lot of other definitions. Many, for example, regard the soul as being the seat of all positive emotions (such as love, nobility, wonder, etc.), with the physical body driving only negative emotions. Or others regard the soul as being the seat of emotion altogether, with the physical being incapable of such things. To people with this kind of dualistic outlook, to not have a soul is to be capable only of evil and selfishness in the first case, or merely an automaton – a thing rather than a person – in the second.
So when an atheist says something like “I don’t believe in souls,” many people don’t hear “I don’t believe in an immaterial component of consciousness that survives outside a living body.” They hear “I don’t believe in positive emotions, only selfishness and evil.” Or they hear “I don’t believe in behaving like I or anyone else is a person.” A lot of these people, though, would probably say that atheists have souls, but are just mistaken about it.
Some even go a step further than that. Either out of desire to demonize atheists, or simply an inability to comprehend that it’s possible for people not to believe in souls, they will twist the simple statement “I don’t believe in souls,” into something like “I want to destroy the soul so that everyone can be purely selfish and/or automatons.” These people are a lot more likely to say atheists have no souls (or that the “atheist ideal” is a “human form without soul,” as I recently read in an incredibly ignorant article about how us atheists would all love to be vampires), because what they mean by that is that atheists are bad people. This is especially true for those looking to demonize us, since to them and their target constituencies, the accusation of soullessness brings to mind images of dead-eyed, leering monsters in human form setting out to debauch themselves and harm everyone else in the process.
But when an atheist like me says that he doesn’t believe in the existence of a soul, he’s not saying that he doesn’t believe in the impulses to love, or empathize, or create, or wonder, or any of the other positive emotions and impulses commonly ascribed to souls. There is, after all, nothing that logically requires those impulses to be bound to an immaterial immortal consciousness. Our lived experience is still a human experience just like everyone else’s and doesn’t become qualitatively different just because we don’t credit that experience to the same source.
We just happen to think that all of those impulses – the good and the bad (and justifying the use of “good” and “bad” is probably a whole series of posts on its own) – are all rooted in our material bodies. It’s all inseparably human.
It would be nice to think that we have a “true” self that is upright and good and will someday be free to live forever without being dragged down by all the bad parts of ourselves when we leave our bodies behind. But the reason I don’t believe in souls is not because I think it would be great cease existing, or because I really want to cling to the bad in me. It is, quite simply, because I’m not convinced that that souls exist.
So this is me, all of me, here in this world being soulless and human just like anybody else.