algebraic topology – Homotopy between inverse path

I’m really struggling with some exercise my professor left me about fundamental group so I think I need some clarification.
During one of them I found that any loop $omega$, where $omega$ belongs to the fundamental group of a connected space, it is homotopic to its inverse $omega^{-1}$, but what does that means?
In my opinion the only way that could happen is that they are both contractible. Am I missing any other possibility?