The subject of the existence or nonexistence of the "spirit" or Soul is a prickly one for most people, throwing them into strictly black and white camps. To my mind it all boils down to how you define Soul. Some view the Soul as a non-material "self", others as the "Ground of Being", others as "wishful thinking" powered by the fear of nonexistence...to me it is none of these things.
For a man like myself, once branded a Secular Humanist by zealots, once called a "Spiritual Atheist" by a friend, it's a tricky proposition. Just because I'm a secular humanist doesn't mean I'm not spiritual. I'm of the manifest understanding that the Universe of time/matter/space/infinity is itself sentient, though not a Deity by any means, it just is what it is...more like a Mind, if you prefer - though this Mind is as beyond ours as our mind is beyond a Praying Mantis. I believe that "religious experiences" of "Universal connection" or "Universal equivalence" or even more mundane epiphanies are junctures where we participate in this Mind, or Soul, for a frozen moment and the illusory self we cling to is momentarily overcome.
We are fractal fragments of that Mind, or Soul, our patterns reflecting those of the larger whole - the Universe itself. Another applicable analogy would be that of a hologram. Like a shattered hologram, each piece shows the original image but with less detail. This Soul we are all component parts of is in no way connected to what we mistakingly perceive as Self - the collected chemical baggage of opinions, attitudes, beliefs, memories, hopes and fears encoded in our brains during our brief series of cycles around the sun.
We are the concious, self-aware expression of the Infinite, dancing at the bottom of a gravity well, blind to who and what we are - the Universe itself - our heritage, birthright and Soul.