For proving that L is in NPC, why do we reduce a known L' into L and not the other way around?
Saying that a problem is NP complete is, approximately, saying that there is no good algorithm for it.

Saying that $L$ reduces to&nbsp;$L'$ means, approximately, that one way of producing an algorithm for&nbsp;$L$ is to use an algorithm for&nbsp;$L'$ as a subroutine.

Now, if $L$&nbsp;reduces to&nbsp;$L'$ and $L$&nbsp;is has no good algorithm, then we know that $L'$ also has no good algorithm&nbsp;&ndash; if it did, then "use&nbsp;$L'$ as a subroutine" would be a good algorithm for&nbsp;$L$, but no good algorithm exists. However, if $L'$ reduces to&nbsp;$L$ and $L$&nbsp;has no good algorithm, we know that "use&nbsp;$L$ as a subroutine" isn't a good algorithm for&nbsp;$L'$ but so what? There are infinitely many other algorithms and we know nothing about whether those are good or bad.