Answer:
Spare the cane spoil the child means if you don't disapline your child then your spoiling them
The bible phrase is actually: "He that spareth his rod hateth his son: but he that loveth him chasteneth him betimes (diligently)."
The Hebrew word was shiavet, which means scepter or authority. If you choose scepter in your translation, you can then consider that scepter is a big stick (rod) and leave it at that. If "authority" is what was meant, then the conclusion is different.