We jokingly put these types of things in memes or in comments, but is it really a joke?
These phrases were the start of my mental illness. I'm not blaming my parents, I don't think, but when a person is crying and you tell them you'll give them something to cry about, it moves the validity of what is making them cry over to being afraid of whatever punishment for crying may be given. They're having a new fear added to their fears. When telling the child that the other person is going to be more harsh with punishment instilled fear of that person more than of what the punishment might be.
We are essentially training our kids behaviors, fears, likes, and dislikes.
I will never claim to be the perfect mother. I want my kids to feel safe coming to me when there's trouble, know that I can help them without someone else leading the way. I have never said they should just wait until their father gets home in a manner of eventual punishment. Punishment isn't always the answer. Discipline works better.
I teach my kids right from wrong by actually discussing the situation at hand. Praise them for the good, but also explain why the action or behavior is unacceptable when it's bad. It's repetitive. Exhausting. But it's worth it.