The Bible does indeed teach that every human being has a spirit, but that spirit is neither immortal nor a soul.
I. The Spirit in Man
We discuss the biblical concept of the "spirit in man" extensively in our free booklet, "The Theory of Evolution--a Fairy Tale for Adults".
In this Q&A, we are quoting the following excerpts:
"You are the light of the world. A city that is set on a hill cannot be hidden."
-Matthew 5:14