This is my "geometric freshman explanation":

the problem is to put something instead of the "?" doing the job of $s$ in


![alt text][1]

[1]: http://img841.imageshack.us/img841/9651/outy.png

...but the composition $\eta\circ\epsilon$ is disconnected, and there is no way to obtain a disconnected manifold starting gluing something to that. :( such a pity.