Why $y[n] = x[-n]$ is not time-invariant? I followed these steps, but the answer still says that this system is time-invariant

let: $x_2[n] = x[n-k]$

$$\begin{align}
y_2[n] &amp;= x_2[-n] \\
 &amp;= x[-(n-k)] \\
 &amp;= x[k-n] \\
\end{align}$$

and 

$$\begin{align}
y[n-k] &amp;= x[(-(n-k)] \\
 &amp;= x[k-n]
\end{align}$$

where am I wrong in the analysis?
A time-invariant system is one that, when you shift the input signal, the output is shifted by the same amount.

A system that reverses the signal cannot be time-invariant because when you shift the input, the output is shifted the other way. $k$ and $-k$ are not the same amount.

$$
y[n-k] = x[k-n] = x[-n \mathbf{+} k]
$$