Buy that saying is lie. It is simply not true. It is just something said to kids when adults don't want to deal with situation. It is good for adults to say that, because then they can continue to watch tv unbothered.
Words to affect people and if you don't respond to insult, you will be bullied and insulted more and more. You will not have respect and you will lose ability to influence what is going on with and around you.
In addition, men used to hold duels over words, so it was not even historical standards.
> When someone took offense we told them to "grow up."
Yes, some adults were enabling bullies like that. Especially if they themselves did not like the target. But it still was exactly that - enabling.
Just letting it go or being submissive is not functional strategy to deal with these issues.