In a basic theoretical model excluding things like individual holders, short term speculators and stocks outside of the index, if you add up all the active fund

In a basic theoretical model excluding things like individual holders, short term speculators and stocks outside of the index, if you add up all the active funds, then the holdings should indeed match the passive funds (since the passive funds are just holding a percentage of the total, the remainder must hold the remaining percentage). So in this toy scenario obviously active funds would underperform after fees. But there's more reason for investors to pick stocks than just beat the market (risk preferences - for a lot of people the benchmark is not the S&P but bond yields). The majority of active management is not hedge funds and are not in the business of providing outsized returns (especially not to small retail clients). To beat the market, one must take risks that the other active managers or index committees deem to be unacceptable.