tangent bundle that isn't diffeomorphic to the Cartesian product

Question

I am studying the notion of tangent bundle $TM$ of a smooth manifold $M$,and in my textbook I am acknowledged that for most smooth manifold of dimension $n$,it's not true that $TM$ is diffeomorphic to $M \times \mathbb R^n$.I failed to give a simple example.I noticed that there is a set-theorical bijective correspondence between the to space,which makes it more difficult to understand why the diffeomorphism fails in general.Is there anyone to help?