Are you saying you do not believe we have spirits?
Do you not believe that we have spirits that live on after the death of our bodies?
The Greek 'pneuma' is translated 'spirit, wind, breath, etc.' What do they all have in common...invisibility.
We don't know what 'spirit' is, but it is like 'breath, wind' in that it is invisible.
GOD has given us an analogy of things that we know, 'wind, breath', in order to give us understanding of something we don't know, 'spirit'.
Yes, I believe we have a spirit and it is the invisible, non-tangible core being of us and it is bodiless unless inhabiting this body or a different intermediate body supplied from above until the resurrection.