OK I’ll take a bite at this.
Yes the argument is going to hinge on the definition af “social injustice” There can be no narrow definition of oit nor can there ever be an accurate measurement of it.
The anti capitalists at the end of the day mean that under capitalism some people make more money than others. They call it many names. They call it exploitation, they call it racism, they call it greed, they call it inhumane, they call it cruelty etc. the list is endless.
What they mean is they read in the paper that person A (like Bill Gates or Donald Trump) made a kazillion dollars last year- and he seems healthy, gets to travel, lives in a crime free neighborhood, has great medical care and is not hungry.
Then they see in the news media, reports of hungry people or people that live in crime rich areas or of people who die of insanitary conditions or AIDS and cannot afford medicine. Mentally they calculate that there is a huge “gap” between these two groups. It does not take into account the millions of people in the middle or the people that were at the bottom but have an opportunity to get to the top.
And then very strange conclusions are made, like : the person at the bottom suffers “social injustice” because of the person at the top, and therefore the only convenient explanation is capitalism.
There are too many fallacies in that argument to try and counter it with evidence for or against "social injustice " in capitalist societies.
In the same vein it can be said that education or practicing a sport or a skill inevitably “leads to social injustice”. Therefore we should create a system where people are banned from getting “ahead” of others in ANY fashion and those that do, should somehow be punished.
On ANY scale including income, there will ALWAYS be a low end.
So for instance quadriplegics will never become soccer champions and people in a coma will never solve the worlds mathematical problems.
In the same vein, there will always be a low end on the income scale. But as a society evolves and improves and gets more efficient and grows more wealthy, the upper level will forever go higher and higher. Therefore the supposed “gap” will always increase in a free society.
That is why new records are being broken at the Olympic games every time. It is not because the system involving “practice” or “coaching” leads to social injustice.