I remember a story my mom told me from when I was about four or five. We were visiting some family friends, and when my dad said, “Well, we have a few things to do and some places to go,” I interrupted and said, “No we don’t —we’re going home!"
(Or if you have kids and don’t mind sharing a funny story)
I always found it very puzzling as a child how parents thought we were supposed to read their minds to know what they were thinking. A story similar to the above: the family was on a road trip vacation with a trailer, from Portland, Oregon to Yellowstone. I think the second night’s stop was at someone’s house in Somewhere, Idaho, and (because my father likes to drive and drive) we got there after dinner time, although we hadn’t stopped for dinner. My sister and I didn’t know these people, so we waited in the trailer and they went in to chat. They stayed longer than I think they expected, so my sister and I went in and made it known that we were hungry. Apparently our parents had told them not to go to any trouble and that we (the family) had already had dinner. So we exposed their stupid lie and embarrassed them, and of course we were the ones they were angry at.
Let’s see, another time at Thanksgiving dinner with extended family hosted at our house, I said out loud that for dessert I wanted mince pie with rum sauce. I got all kinds of flak because my great-grandmother was Dry, something which I had never been told. I got yelled at anyway.
When I was 11(ish..I forget exactly) I was being a little shit at the dinner table and my dad called me a son-of-a-bitch. I immediately shot back that he should not talk about mom that way.
There was a collective pause at the table. Then, somehow, everyone collectively decided to ignore it and move on. Even the dog was thinking, “Did he just say that?”
When I was 3 years old or somewhere around that age, my mother didn’t want me running around in the airport, so she put me on a leash. I then promptly got on all fours and started crawling like a dog. The onlookers laughed so hard and my mom was so embarrassed that she took the leash off.
You weren’t wrong to call him out on that.
When I was 7, I and my younger siblings would call my mother out for lying about her age in public. She stopped doing that pretty quickly.
When my son was little we were at a public place with lots of people around. He goes to me and points to a lady next to us and says “look how fat her arms are” (they were really fat). I tried to stop this conversation but he thought I just didn’t see them. He was very insistant that I notice her arms and comment on them.
I never embarrassed my parents because I was an enchanting and quiet child. My children were much the same. However, I do remember one time when the boy was about four. We were in a public waiting room when a teenager came in sagging some ridiculous giant pants (as was the style at the time, this was somewhat after the onion tied to the belt thing). My boy started pointing and laughing, saying, “Mom! Clown pants! Why is he wearing clown pants?”
On second thought, not that embarrassing. I told you he was enchanting. 
My mother held a party for family and friends so I got some tabloid mags from the checkout at the grocery store like the Weekly World News and the Enquirer and put them out on her coffee table along with the snobby coffee table books she put out there. Everybody loved reading those things back then before the gossip and fake news were readily available on the internet. Wasn’t long before mom noticed - “Where on earth did those come from?” and took them away.
My brother climbed a tree, and did the classic “look mum, no hands” with the predictable result.
Fortunately he did not break any bones.
My mom lied about her age (by one year!) for soooooo long. Still don’t understand it. Maybe I’ll bring it up next time I see her 
Someone once asked my grandmother her age.
Grandma: “65.”
My uncle: “Momma, I’m 62.”
Grandma: “You big liar!”
I have no memory of this, but my mom told my that, when I was a toddler, she took me with her on a trip to the post office. (I should mention that my family are all pale Caucasians.) As we were standing in line, an African American man walked by. I gave him a big smile and said “Daddy!” Mom was not embarassed, but he was mortified.
Not sure what circumstances the OP is asking about. The gossip mag prank I mentioned was something I did intentionally to embarrass my mom. So many things I did without intent to embarrass still embarrassed her, or made her angry, or both.
A woman I know told me that when she was maybe 4, her parents were hosting the minister on Sunday afternoon. She decided to be helpful, so carried out a tray of martini glasses filled with water, like she’d seen her parents serving at parties.
One time we had guests over for dinner and my mother told me beforehand to go easy on how much I ate of a particular dish (I forget what it was). Then during dinner, someone offered me a second helping of that dish and I declared that I couldn’t because my mother had banned me from eating it.