So I'm still not clear on what Peterson means with "growing up" but googling it seems to be about taking responsibility. I actually wrote a small article on that a few years ago and still stand behind its conclusions, so I thought I'd share it.

Conflict resolution in modern societies through legal recourse inherently favours injustice over justice, in the long run. The belief that social justice is attained through a strong and independent court system is false, in the sense that it is incomplete, and there are various processes that cause this. The consequence is that, if a society as a whole considers social justice in its broadest sense, it must pursue more than a legal framework for conflict resolution. It also requires (affirmative) action by society at large, where we actively take responsibility for those injustices we did not commit and for which no legal remedy is (any more) available.

Of the processes that cause injustices to be perpetuated, and sometimes even be aggravated, I will consider the following. First of all, law systems are increasingly unable to cope with the sheer amount of legal disputes. This has driven up costs, making court cases and the legal profession more expensive, due to high demand and a closed system of accreditation (requiring patronage, membership to the bar and similar barriers), and consequently inaccessible to many. It therefore favours the rich and corporations, where the latter even receives a tax benefit as it is calculated as a loss against profit before taxes.

Statutes of limitation further limit which claims can be brought before court; we can only pursue a claim for a certain period of time. This means that for a variety of reasons, old claims no longer are legal claims but merely moral claims, which the State does not enforce. As just, moral claims are not resolved, injustice is perpetuated. That is not to say that statutes of limitation should be removed. They are important procedural rules to economise the court system and ensure a decent level of efficiency, without which the court system would quickly be flooded with impossibly old and difficult cases. Moreover, modern law is more concerned with effective conflict resolution than justice. The law has become an economic tool (e.g. effective regulation of market fundamentals, in particular property rights) instead of concerning itself with enforcing social justice. In other words legal solutions are not necessarily just solutions as effectiveness of enforcement or protection of particular economic interests has become an important driving factor.

And, finally, changing concepts of social justice may mean that actions in the past are considered injustices by today's standards. By these modern standards, these past injustices were not adequately compensated. Most prominent examples thereof would be slavery, misogyny and colonisation.
These ideas led at one time or another to a near total socio-economic disenfranchisement of blacks, women and indigenous people. Not only was their loss another's gain; these losses and gains have been perpetuated through a legal system that understandably does not criminalise acts with retroactive effect. Moreover, although inheritance law recognises the transfer of legally recognised (monetary) claims offset against the benefits, it does not recognise the transfer of moral claims. These morally wronged people had no recourse but neither do their descendants, while those who (by modern standards of social justice) unjustifiably benefitted from the wrong and their descendants continue to benefit.

If we then remember the adagium "it takes money to make money", it is clear that a basic inequality sets in where, within a given State, blacks and women (and other minorities) continue to be at a socio-economic disadvantage; simply because they are not afforded the same opportunities as dictated in large part by their socio-economic background. Contrary to popular belief, the most influential predictor of socio-economic mobility is not a person's education level. Instead, the strongest correlation between a person's life chances in society and economic mobility is how economic status and inheritance are transmitted across generations. The children of well-off parents simply tend to receive better schooling and benefit from material, cultural and genetic inheritances as researched by Bowles and Gintin in The inheritance of inequality.

On average minorities and other generally socially disadvantaged groups receive less inheritance and wealth and thus more often rent homes, live in poorer neighbourhoods and achieve lower educational levels compared with people from better socio-economic backgrounds. Moreover, due to the stratification of social classes, the rich intermarry with other rich and the poor with other poor. In other words, there is a division along social class in which wealth is protected and transmitted across generations through inheritance, reinforcing and perpetuating socio-economic privilege for the rich.1

As becomes clear, inheritance inequality, together with past social injustices, is the cause of continued socio-economic disenfranchisement of minorities and, when considered at the international level, even entire countries and regions. Despite this, there is a tendency in the West to consider that we have made much progress socially, politically and morally in the past 60 years but the reality is, we only pay justice lip-service. In the West we agree that discrimination is wrong but we do not put our money where our mouth is. We stopped slave trading, we stopped colonisation, we accepted women as equals on paper but then make no effort to undo past wrongs. We did not relinquish the considerable profits we made from the exploitation of others and then puff our chests in self-righteousness and expect minorities to be grateful for our magnanimity.2

Having established that social injustices occur and/or exist for which the law not only fails to provide recourse but even reinforces them, we must turn to politics as the broadest arena in which power and social relationships are shaped. When doing so, we are immediately confronted with the obvious counter argument that current generations cannot be held responsible for crimes committed by past generations, because they are in no sense guilty and that the guilty themselves are long dead. This is true when we accept a narrow definition of responsibility but it is my contention that we already accept, in many areas, a broader concept of responsibility and that there are no good arguments to deny them in this area.

There exist a variety of social injustices today in which others than those who caused the injustice, take responsibility. We do this constantly, in fact. We do this for the weakest of society through monetary support but also with, for instance, orphans. When a neglectful family abandons a child, this is not through action or inaction by society. Society at large cannot be considered guilty. Yet we do not abandon these orphans. As a society we take responsibility for such an injustice through orphanages and adoptions.

When one person commits a crime towards another, or intends to, society at large has no responsibility either. The crime is that of the criminal. Yet through police action we take responsibility for the situation and try to defend the victim from injustice. Society is mobilised to help the victim find, judge and punish the criminal. As it is, we continually take responsibility for social injustices for which others should (have) be(en) held responsible. Aside from a broader concept of responsibility, there is also an asymmetry to the counter argument; why accept all the benefits through inheritance as a moral entitlement but not accept moral obligation towards moral claims from the past? In other words, from a moral standpoint to believe entitlements exists but obligations do not, when they stem from the same occurence, is entirely arbitrary.

When we return to Bowles and Gintin's research we see that the inequality affects a wide variety of aspects, such as but not limited to education, housing, job security and health. Similar to the meta-ethical distinction between negative and positive freedom, it is not sufficient to merely remove the shackles (as we have done in the past) but also to offer opportunity by providing good education, housing and healthcare for minorities. The men or women, who do not have a choice due to lack of opportunities, are no freer than when we would forcibly restrain them. Taking responsibility then means creating opportunities and that implies affirmative action in a variety of areas to improve the socio-economic mobility of citizens and ultimately increase their freedom of choice.
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*1 It also leads to a more general form of income inequality which strongly correlates with health expectancy as well; more so than actual levels of poverty.
*2 There's another philosophical point there that the white man "gave" these rights; they granted the right to freedom, they granted the right to independence and, to a lesser extent, granted the right to vote. The power relations have not changed much since the end of slavery and women's suffrage.