A very good question; and I don’t think there is a simple answer, or a single main cause. Wealth inequality has existed since the time humans stopped being ‘hunter gatherers’ and started to farm the land. These days, factors affecting the level of wealth inequality in ‘Society’ include greed, prejudices, ignorance, fear, differences in individual abilities, motivation, work skills, education and training, aspirations, mental health, disabilities, luck and privilege of birth etc.
The political system can be a force behind expanding wealth inequality. Put in simple terms; the policies of ‘Capitalist’ governments in modern Western Democracies tend to favour the rich getting richer (all too often) at the expense of the poor; albeit, when in power, Socialist governments will attempt to address the imbalance with their political agenda e.g. by making taxation more equitable to the benefit of the less well off, and through other ‘Social’ measures to provide the greater need where its most needed.
For example, in Britain to help people on low income, and narrow that wealth inequality, the legal minimum wage is currently £7.20 ($10.20) per hour, with no one paying any ‘Income Tax’ (which I think in America is called Payroll Tax) until they’re wages exceed £11,000 ($15,562) per year’; with the next tax bracket on wages above that level being 20%, and the highly paid employees paying 45% on income over £150,000 ($212,230) per annum.
And as an added aid to the low paid, they are also paid ‘Working Tax Credits’; money provided by the government to boost the income of working people who are on a low income e.g. the government deposits up £1,960 ($2,773) per annum (paid monthly) into your bank account, reducing on a sliding scale until you’re wages go above £11,000 ($15,562) per year.
Of course in other parts of the world where Regimes still exists e.g. Monarchies, Right wing Dictatorships and Left wing Communist governments then wealth inequality (often driven by greed, prejudices, and corruption etc.) are still rife in Society as they have always been since Ancient Times.