classical mechanics - Why must allowable physical laws have reversibility?

I'm watching Susskind's video lectures and he says in the first lecture on classical mechanics that for a physical law to be allowable in classical mechanics it must be reversible, in the sense that for any given state $S\in \mathcal{M}$ where $\mathcal{M}$ is the configuration space there should be only one state $S_0\in \mathcal{M}$ such that $S_0\mapsto S$ in the evolution of the system.

Now, why is this? Why do we really need this reversibility? I can't understand what are the reasons for us to wish it from a physical law. What are the consequences of not having it?