Confusion with the root of “inspiration” & “inspiring”

As I know, “inspire” and “inspirit” have similar meanings , almost the same. But “spirit” means feeling, mind, and “spire” means top of building.

Apparently, “spirit” is more suitable as root for feeling, mind, or other mental relevance. What is funny that neither Cambridge Dic. nor Oxford Dic. includes “inspirit”.

Structurally, “inspiring” & “inspiration” root from “inspire” more probably, but “inspirit” is more suitable in terms of meanings absolutely.

This is exactly where I am confused.