When it comes to souls, I am not committed to believing in their existence. This is to say that I do not reject the general idea of souls, but I do reject one particular theory of souls.
The PMS (Popular Meaning of Souls) theory holds that souls have their own agency: They make choices and decisions, they have desires and needs, they can affect what happens in our brains, and they can be inspired or otherwise affected by kugel, music and so on. This is nonsense. Here's why:
The brain is the source of mental life; our consciousness, emotions, and will are all the products of neural processes caused by those coils of grey matter contained within our skulls. When I make a decision, or walk across a room, or enjoy a slab of kugel those are all physical events both caused and experienced by other physical events, namely the firing of my neurons inside my brain.
The trouble with the PMS theory is it insists that some physical events are the consequence of our souls, but how can something non-physical such as a soul cause our neurons to fire? Proponents of PMS wish us to accept that there are two types of stuff: the physical and the spiritual. They also wish for us to accept that the spiritual stuff can exercise control over the physical stuff. But they offer us no mechanism to explain how the two kinds of stuff interact. It's all a mystery, left to faith.
But why should a Jew leave things to faith when it isn't strictly necessary? Judaism works perfectly well without souls. We are bidden to keep the commandments not for the sake of the afterlife, as if we were Christians, but for the sake of this life. Again and again we're promised that following the law provides benefits in this world. In Tanakh, nothing at all is said about the next world, and what is said in the TSBP can be explained without PMS, much as what the Rabbis said about history, science, medicine and nature has been explained. Be it metaphor, myth, or our misunderstanding or mistake, there's no requirement to take these Talmudic and Aggadic statements literally.
To sum up:
The souls I don't believe in are a particular version, much as I don't believe in a bearded god sitting on throne. I don't feel that expanded definitions of souls fits well with Judaism or our understanding of the world. Furthermore, while a minimized definition of souls does not have these problems, I see no Jewish requirement to invoke them. Finally, even if I'm wrong about their existence, my position on them does not endanger any halakha or encroach on an ikkar or other hashkafic matters.