According to Cambridge dictionary, Capitalism is,
“an economic and political system in which property, business, and industry are controlled by private owners rather than by the state, with the purpose of making a profit”
So the alternative is state control and history tells us that only works with certain endeavours - e.g. military - and can be catastrophic when applied to things like agriculture (see collectivization).
The key element of capitalism is not so much private vs. state ownership, it's ownership (and thus profit extraction) based on capital.
And the effect of is allowing control to be arbitrarily skewed towards wealthy individuals who don't need to work, while leaving others with no control at all, even over the work they do, while still needing to work to sustain themselves. Additionally, this skew tends to increase over time as capital accumulates profits exponentially.
The alternative is basing control on something other than capital. But that actually leaves a lot of different options, not just state ownership. What if the only legal form of corporation were the cooperative, with companies being collectively owned by, and profits distributed to, their employees, equally?