Index volatility is lower than the average of single-stock volatilities because constituent moves partly offset. That relationship depends on correlation, so the trade is fundamentally a short correlation position expressed through options.
It works when stocks behave idiosyncratically, for example through a dispersed earnings season. It fails in a market-wide shock, when correlation approaches one, index volatility spikes far more than the single-stock leg gains, and losses arrive quickly.
The trade is popular enough that its unwinds are a documented source of pressure in the index options market. Position size should assume correlation can reach one, since historically it does so with little warning. See volatility-arbitrage.
Related: volatility-arbitrage, correlation, variance-swap, implied-volatility, index, tail-risk