Whether or not one has a soul depends on the perspective you wish to take on the issue. In this case, I will take con.
It is nothing more than the pitiful desire of our egos that makes us want to believe we have a unique soul -- that we are beings distinct and separate from the rest of the universe. We do this because we fear death, but we also know death is inevitable. An immortal soul solves this problem, but it's just a fairy tail we tell ourselves to comfort our egos.
We have consciousness, but that consciousness doesn't belong to our bodies. To the contrary, our bodies are mere expressions of consciousness, much in the way a wave is an expression of the ocean. To say we are distinct and separate from the rest of reality is to say that the wave is distinct and separate from the ocean. It came from the ocean, it's attached to the ocean, and it will return to the ocean.
It's easier to accept that there is no soul when you come to the position that you don't have to live forever to be happy now.