In their textbook(Example 1.1), Oppenheim and Willsky provide the following method for obtaining $g(t)=x(-t+1)$ from $x(t)$ : Replace $t$ with $-t$ in $x(t+1)$. In other words, advance the signal by 1 unit and flip the result.
But there could be another interpretation as well. Based on the fact that $-t+1 = -(t-1)$, we can have the desired signal as $h(t)=x(-t+1) = x(-(t-1))$,i.e. Delay the signal by 1 unit and flip the result.
But the two signals $g(t)$ and $h(t)$ are not identical. Why is the latter interpretation incorrect ?