2- he claims wealth is passed down from ancestors. He ignores the historical fact that most wealthy people have not gotten wealthy through inheritance. He claims growing inequality is a function of capitalism but ignores all other systems.

2 In fact, from the evidence of 300 years, inheritance has been the main route to hold onto and increase wealth, often by the path of the rentier, holding onto an asset and claiming rent. This ended with that wealth being almost completely wiped out by two world wars, a world financial crash and revolution/fear of revolution 1914-1945. From 1945-mid 1970s, and yes you are correct, wealth was earned through income, but over a certain amount (x30 average income), heavily taxed; inheritance and capital were both taxed at high rates.(Piketty 2017d)

Why?

So society would not become too unequal, and what promoted this egalitarian outlook?

It was the fear of communism, so compromise for the working and middle classes with union representation at the workplace and shareholders (rentiers) at the back of the queue when profits were made, plus CEOs earned no more than x30 national averages due to 90% plus taxation above these levels, so excess profits went back into companies investment, i.e. R&D, better incomes for the employees; thus this period has often been called the ‘golden period of capitalism’. (Piketty 2017a)

So it’s not about capitalism being a flawed system but rather channelled for all to benefit, with a mix of welfare protections when needed and support for capital to grow via government-funded R%D in Universities, infrastructure, promotion for overseas trade etc.— known as a mixed economy.

He talks about the ideals of communism and why it failed, namely the contradictions of such a system. That eventually can only be overcome by either Authoritarian denial and propaganda (think Big Brother in Orwells 1984)or, as in China, a compromise to a form of a mixed economy, but still with a one-party state.