Why does quantum mechanics require time-reversibility and unitarity?

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sadegh4137
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i read a text at www.askmathmacian.com, and i don't understood this

"QM requires that time-reversibility (or “unitarity”, to a professional) holds"

why QM need time-reversibility?
and what's relation between time-reversibility and unitarity?
 

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More transparent statement:

The time-dependent Schroedinger equation is time-symmetric. This means that for any its solution

$$
\psi(r,t)
$$
and any ##t_0## the function

$$
\psi^*(r, t_0- t)
$$

is also its solution.