Spare the rod and spoil the child - Idiom Definition - UsingEnglish.com
I think the idea here is: If you spare the rod, the child will be spoiled, so do not spare the rod if you do not want to spoil the child. (The rod is meant to be used to hit the child (don't do that please, just discipline him/her))
Spare the rod here means something like "save the rod", or "let the rod rest by itself, do not use it, let it be untouched"
P.S.1: Not a native speaker.
P.S.2: I didn't know this idiom before, I have just learned it - "thanks".