Myth: Atheists deny the existence of God, therefore they deny the existence of any soul or spirit.
Response: Belief in souls or an afterlife is more often associated with theism than not, but atheism is nevertheless compatible with belief in souls or an afterlife. I've encountered a number of people who don't believe in any gods, but nevertheless believe in things that qualify as ghosts, spirits, afterlife, reincarnation, etc.
Sometimes this is part of an organized belief system, like Buddhism, while other times a person simply believes in ghosts because of personal experiences. The key to understanding this is to realize that atheism by itself only excludes belief in gods, not necessarily belief in anything else that might be categorized as paranormal or even supernatural.
An atheist can therefor logically believe anything else at all — including souls and some sort of heaven — even if the belief is irrational. This is true whether we define atheism broadly as simply the absence of belief in gods (weak atheism) or narrowly as denying the existence of gods (strong atheism). As soon as you start adding things to mere disbelief in gods, you're talking about some philosophical or religious system that may incorporate atheism, but which is not atheism itself.
Atheism and Materialism
The number of atheists who believe in souls, ghosts, or some sort of life after physical death is probably small — especially in the West. It cannot be denied that there is a strong correlation between disbelief in gods and disbelief in the supernatural generally, which would include souls and spirits. This is because atheism in the West is strongly associated with materialism, naturalism, and science.
The existence of a correlation in a particular cultural context, however, does not qualify as proof of a deeper connection. It does not mean that atheism somehow requires disbelief in anything supernatural. It does not mean that disbelief in gods must always occur in the context of materialism, naturalism, or science. There’s nothing about “atheism” which requires that all of one’s beliefs be materialistic, naturalistic, scientific, or even rational.
Atheists and Materialism
This isn't a mistake that is exclusive to religious theists and religious apologists. Even some atheists have argued that atheism means not believing in anything supernatural; since souls and heaven are necessarily supernatural and belief in them is irrational, then anyone who believes in such a thing can’t possibly be a "real" atheist. This is a bit like Christians arguing that unless someone adopts particular theological positions that have become popular in a particular place and time, then that person cannot be a "real" Christian.
So while it's incorrect to make generalizations about atheism and atheists, it can be correct to make specific claims about specific atheists. Atheists may not all be naturalists and materialists, but the average atheist you meet in the West, and especially an atheist you meet online, probably is a naturalist and a materialist.
You can't derive conclusions about atheism and atheists generally from a premise that is false, but you can suggest tentative conclusions about particular atheists once you take the time to ask them questions and understand what they actually think. You will see the former much more often than the latter, though, because it's a lazy way of thinking and arguing.
The latter not only requires more time and work, it also requires that a person actually be interested in learning about other human beings. It requires treating the person as an actual, individual human being rather than a "type" that can be dismissed without much consideration. This means taking the risk of discovering that they have been wrong and perhaps need to modify their beliefs as a result. Anyone who is at all insecure in their beliefs will avoid this at all costs.