It seems to me the concept of equality is deeply flawed.
Assuming we are all equal is like assuming a falsehood.
It seems that we are all uniquely different.
We are all unequal.
Just look at a crowd of people.
They all look different.
They all have different pasts.
They all have different abilities.
They all have different opinions.

It seems dangerous to start an argument by saying "we are all equal".
In what way are we all equal?

Here is a longer form of the Yaron Brook's argument against equality.

He also wrote a book "Equal is unfair: America's Misguided Fight Against Income Inequality" [amazon.com]

Yaron Brook argues that equality of opportunity is wrong.
Is argument is basically we are different in height, intelligence, wealth, contacts, ...
Wealth can be redistributed but he equates that with theft.
And some things can't be redistributed like contacts.
Are we going to make a law that says you can't use your contacts just to level the playing field.

Is he wrong, and if so how?

If there is be equality of outcome then the outcome will seek the lowest level of input. One can not reliability achieve greater than the best that one can output. Since there is not equality of talent then there can not be an equality of outcome above the least talented.
This is the same issue that is the basic flaw found in Communism.

Equality of outcome, in my opinion, creates misery. Individuals are fulfilled by a sense of accomplishment, overcoming adversity, creating, inventing, giving of time/experience to others, etc. When everyone is guaranteed the same income, job, house, food, clothing, essentials, etc, then we have dampened the human spirit. Is a participation ribbon given to every child as fulfilling to them as a championship trophy they worked hard for? Learning how to handle defeat and winning is a valuable tool that children will use throughout their lives. How can we expect to have any sense of self, if everyone is "the same"? Why strive to be better if it gets you nothing more? Not to say that this topic isn't complicated, I'm sharing a very small point in a broad discussion. Just my quick thoughts.

The Soviet Union and China under Mao and now Venezuela under "socialism" were great examples of equality of outcome: an ebb tide strands all ships equally.

Equality of outcome is unachievable because of the simple fact we are all unique. Therefore, in any given situation one will be better than another. Equality of opportunity we have done well, more work to do, but the strides we have made amazing. In fact, it's just been reported that Google has actually been paying some women more then men doing the same job. Appears the men now have a glass ceiling.

I find it a very intuitively satisfying idea that falls apart on close inspection, and ends up being neither entirely right nor wrong - and so only weakly helpful.

If you define equality of opportunity simply as formal equality within the institutions of society, the idea does very little political work.

The crux of the political struggle includes both formal access to institutions, and the social conditions that define different “starting points” for different segments of the population. So the definition of “equality of opportunity” is deeply contested.

In that contested field, insert the Janus-faced character of opportunity and outcome. Do we give everyone access to good education, and call that an opportunity that we equalize? So their graduating grades would be the outcome we don’t equalize?

Makes sense, but if there is a hierarchy of school quality, and there always will be, then admission to a good school in the first place is an outcome awarded on merit (supposedly) - not an opportunity we equalize.

Do we give everyone access to the best prep schooling, to compete on merit for admission to the best schools? Is that an opportunity we equalize, or is access to prep schooling an outcome of some other (supposedly) meritocratic process?

I’ve held some senior positions in organizations, and consulted within them afterwards. In high-potential (HiPo) programs, people who show promise as future senior managers are rotated through all kinds of positions to learn different areas of the business.

This kind of thing also has an intermediate status between outcome and opportunity. No outcome is certain yet. It’s a development opportunity, but the programs are highly selective. It’s both.

Does desireability of opportunity mean access to it is an outcome? How far back into the preconditions of the inequality of outcomes do you have to go before we hit some bedrock of opportunity (something that is unambiguously an opportunity we can equalize)? Generations?

If you try to simplify it and say “everybody should be treated the same with no reference to race or gender”, you can, but you make no progress with people who think a lot about reasons for the opposite view.

If you reject the idea that inequality of opportunity goes back generations, and you want to convince people about that, then we need sharper definitions of opportunity and outcome that take historical arguments about intergroup injustices into account, and dispatch of them In fully articulated ways.

The opportunity/outcome dichotomy at the heart of this idea just isn’t as crisp as it seems. It’s a mushy analytical concept, even though it’s a great aphorism.

I feel like there is something here that hard philosophical reasoning might fruitfully illuminate. But I don’t pretend to have done this work.

To give the aphorism bite, it would need a PhD’s dissertation worth’s of analysis behind it, I feel. Especially if this idea is to be usefully used to reform policies and laws in ways that enjoy enough social license to become widely and enduringly institutionalized.

So for me it’s a bit more useful than “power to the people”, but it is closer to that saying then it is to a well-justified policy principle that can be widely instantiated in ways that will survive legal challenge.

I’m an educator now, and I definitely want to grade people based on actual work, and not modify those outcomes for other reasons, so I’m not hostile to the spirit of the idea, not at all. I hate grade inflation, and lame excuses for shoddy last-minute work.

But that’s not a very controversial opportunity/outcome judgement scenario. When I try to apply the opportunity/outcome principle to contexts and questions where it using it would actually be controversial, I don’t see it settling questions in ways that would stabilize and become generally accepted.

A definition or a viewpoint?
Eq of Opportunity - give everyone a chance, regardless of their identity, allow the best to succeed, maybe result in inequality of distribution of resources or wealth - i.e. fair competition
Eq of Outcome - everyone should get a chance but maybe the opportunities weren't equal, so some further equalization might be necessary to establish equitable distribution (equity) of resources and wealth - i.e. quotas
Opportunity - It is very hard to establish a truly fair competition, after all bias really does exist. But we have probably never seen a more egalitarian society, so even if not perfect we're getting there. Social and cultural improvements can and need to be made, so let's keep working at it.
Outcome - While equitable distribution might sound fair, the real problem is who decides? The government? Do we really want the state declaring one race, or gender, or orientation, or religion, as more dominant or oppressive than another, thereby picking winners and losers based on their sex, skin colour or creed? There is no way to get around the fact that in order to implement Eq of Outcome requires a gov't authority saying who is better than others. As much as I'd want us all to do well, I can't see how gov't Dictating who prospers and who needs to be taken down a notch can lead to any good. There will always be people with a different ranking order, so who gets to choose?
I believe in regulations to help keep the selection process fair, yes, but dictating position based on identity instead of merit is a horrible role for government to play.
One should always want the best person for the job, regardless of who they are. If we could teach people that, there'd be no need for quotas.

I think jail is the closest approximation we have of "equality of outcome." Everybody gets pretty close to the exact same things.

(Yes, I know, different jails are different. But within a single jail, everybody gets pretty much the same treatment. I didn't say it was a perfect example.)

Equality of opportunity means we all get the same chance at an opportunity or right in society. Say equal acress to vote or apply for s job. Equality of outcome suggests that the inky thing that matters is that we are equally represented in jobs. But that also means affirmative action so that the best candidate do not necessarily get the job but rather someone who has been underrepresented. So perhaps an Asian person or a person of colour and not a white male who may be the fastest to climb the latter as a firefighter, but who is over represented. I feel that we should strive for a society where regardless of sex, race or political views, we can be considered for an opportunity. If that means more black people end up on a basketball court because they were the best for the team, then they should not be denied the opp just because there are more blacks than whites in NBA. Those selected for an opportunity should reflect the best appointments to those roles rather than an exercise in having an outcome of diversity. Equality of outcome seems impossible. There is no way to make things equal for everyone. Plus you would also need to steal from the rich and give to the others to create the equal outcome. Bad idea. Better to give everyone the same chance to an opp and those who work hardest get the prize. Same chance for everyone !

No such thing as equality of outcome, not in my opinion anyway. As for the latter? In the US there is opportunity for all who seek it out.