Do you know what one of my (many) pet peeves is? The phrase "you'll understand when you're a mother." As if being a mother magically makes you perfect. It doesn't. In fact, sometimes, it makes you more annoying. Because your brains are all jumbled from being responsible for somebody else's bodily fluids.
Case in point: yelling at your child for doing something rude to a stranger without apologizing to said stranger first.
I don't blame kids for being annoying. Kids are inherently annoying and don't know any better. I think God made them that way so that people wouldn't want to have a zillion kids. That's why the Duggars have so many. For some reason, Duggar children weren't born with as big of an annoying gene as normal kids and so their parents don't have the need to stop having them. This is just one of many theories I have about the Duggars.
So your kids runs in front of a stranger. Yes, it was rude, but the stranger, though childless, does not blame the child. Because it's what kids do. And now, it's the parent's job to correct the kid's behavior. Again, the childless stranger understands this.
However, if you yell at your kid and don't say anything to the stranger, it makes for an awkward moment for the stranger. The stranger is left standing there, watching you yell at your kid, knowing that they are the reason the kid is getting in trouble.
But! If you apologize on behalf of your kid before you start yelling at your kid, the whole awkward situation disappears! Because then the stranger can say "oh it's no problem!" all friendly-like and not have to stand there as if they're the ones who did something wrong while you chastise your kid.
This public service announcement brought to you by a Hornbuckle who will understand why it's okay to be rude in public when she's a mother, I guess.