If it was for the middle finger only, then I don't see what the problem is. If that (the middle finger) is the reason, it's none of our business, period. (And I don't understand why the cubing community is talking about this at all.)
This post is assuming that at least part of the reason was for the middle finger, and it's directed only at the individuals who think that what she did was wrong and that she needs to apologize for it.
What Changed in Parenting Over the Years?
I don't know what changed with parenting in the past few decades that parents disciplining their children is somehow a crime (well, lawyers are ruining the world, so they are probably the cause, no matter how indirect... they are trying to make anything a crime so that they make more money).
For the parents reading this (or for anyone who is thinking about being parents someday), are you all the type of parents (or wish to become a parent) to let your child touch a hot stove so that they learn that it's hot when they get burned? Or do you think it's better to slap them if they persist on touching it when it's hot? Or slap them to stop them from running into the middle of the street... or letting them get hit by a car so that "they learn their lesson"? You can't talk/persuade children out of doing something all the time. Some are really persistent/rebellious/curious.
And why am I comparing the middle finger gesture to getting burned by a stove or hit by a car?
If a little kid makes an offensive finger gesture at the wrong person, that person can grab the finger and brake it. (Or worse.) I know of a personal story that one of my male cousins here in The United States of America who, when he was about 10 years old, flicked off a grown man at a restaurant, and that grown man grabbed and broke his finger! What's worse? One slap on the face to potentially stop a lifetime of flicking people off (and all of the potential consequences for doing that) or a broken finger?
That's why I am saying that! It's offensive! Duh!
If the kid was covered in marks and bruises, then sure, you all would have a case to say of how much of an abusive mother she is. Another cuber mentioned "if she does something like that in public, imagine what goes on behind closed doors". The kid would be covered in bruises if much worse happened behind closed doors.
Just because we saw her hit him in public, that doesn't mean that she frequently hits him behind closed doors. It's the same as if you curse in public because something really bad happened at that particular moment, so everyone around you assumes that you curse like a sailor at home... does that make them right? (For some people they would be correct, but not for others.)
Furthermore, this may not at all been the first time that he flicked someone off. And you don't know that for sure to judge her that she wanted to put a stop to it. If she is as "corrupt" as what you all believe, she would have waited to beat the tar out of him when they got home so that she could continue to "abuse" him as you all think she does. (Abusers want to keep abusing... not put themselves at risk of getting caught so that they are "brought to justice"!)
She slapped him once with her hand (not an object which would give leverage), and his head did not tilt downward in the opposite direction of impact to think that she hit him that hard.
In addition, she may have commanded that he turn around, and he refused (rebelled). That's what I can see from before the hit. Clearly she was expecting him to turn around and face her. He refused, so she hit him with the angle that he gave her. You cannot assume that she wanted to hit him on the ear like that. I am mentioning this, because someone on rcubers said that "she could cause permanent hearing loss". If she hates him so much, don't you think that she would want him to be as less dependent on her and his father as much as possible as fast as possible? Intentionally inflicting a physical disability on him would be the last thing on her mind (making him dependent on them or society, long-term)! She would want him out of the house ASAP, wouldn't she?
The Result of the Change in Parenting Over the Years
In the real world, people kill each other for much less offensive things than flicking each other off... Brush up on your history (and observe the world around you.. get out of lala land). You will find that people got killed basically just for existing or being in the wrong place at the wrong time!
Could there be a better way to discipline a child than hitting them? Many modern day parents make threats to take away something that's the child's one joy in this world as a form of discipline. If I had to choose to get slapped or get something that I love get taken away from me, I would choose the slap without a question. Because it stings for a minute and then it's over. When what I have gets taken away, that thing can be taken away for a long duration of time (or forever). And being afraid of getting threatened opens up all forms of anxiety. My nephew was never hit once in his life, but he acts like his parents hit him a million times... (that parenting approach is clearly NOT healthy for the child).
Verbal threats can be much worse than a slap, if we want to judge her as a bad parent (overall).
Notice that I didn't say "verbal abuse can be much worse than physical abuse". Abuse - treat (a person or an animal) with cruelty or violence, especially regularly or repeatedly. We don't know how frequent she hits him. But I wouldn't define doing something minor to someone (compared to what could happen if that minor hurt was not inflicted) as abuse, especially that the very nature of her actions was to correct him!
Bigger Picture:
All in all, when you all discover the secret to have world peace without any threats or force, then you all can be a judge for how someone who is doing her best to ensure the survival of her child. Until then, can the community talk about something else?
Don't let the convenience of the internet news today (that lets you see what happens world-wide 24/7) deceive you into thinking that all cultures are the same (or that they should be). Condemning an entire culture because they are different than yours is what starts wars (and is downright arrogant). If you all are about peace, then you need to seriously think about that.
Insisting that she apologize for doing her job is downright insane!
That's my 2 cents on a matter that I am surprised is becoming such a big deal that cubers on reddit are debriefing others who have returned from a cubing hiatus that that is one of the things in cubing history that has happened since he has been away from cubing!
If I get slapped for doing something wrong today so that I don't get killed for doing it later on in life (to the wrong person), I think I would be grateful for the slap today!