The socialist option is to deny individuals the right to own personal capital at all to prevent said inequality, and instead to create a system to allocate capital in a way that is best for society, i.e. through the government. But it turns out that all the ways that society requires capital are practically beyond counting, and the system is so complex, that any government looking to even be minimally successful in overseeing that allocation process requires large amounts of power over virtually every aspect of society. Guess what? That's authoritarianism.
Take this thought experiment. Say we decide we want to make a new entertainment service to compete with Netflix. But creating it requires capital: money to pay programmers, money to pay for servers, money to pay for content production, etc. In a capitalist society, we just have to convince enough people that there is enough return on investment to give us their money. They don't even have to like watching TV, they just have to be convinced its a good use of their excess money. And they could be millions of people, or it could be a single individual. On the other hand, in a socialist society, we have to convince the proxy for society in charge of doling out society's collective capital (i.e. the government) to give us their money. So now the decision on what content to produce is directly influenced by the government. Even if these people are democratically elected, they will cater exclusively to the majority opinion, and in the more likely case, they will cater to whatever consolidates their power. Oops! Now you have state-controlled media. Seems unlikely the people controlling said media will devote much air-time to opposition parties or ideas, or that your functioning democracy will last very long in that scenario.
The point is that socialism without authoritarianism is a paradox. Socialism cannot function without authoritarianism, because the process of allocating capital in society is far too complex for a reasonably constrained governmental body to undertake. It needs an authoritarian level of power to effectively manage society's capital (and as history shows us, even then it rarely is actually effective). Insisting on non-authoritarian socialism is like insisting on a diet consisting exclusively of ice cream and cake while also living a long, healthy life. Perhaps it sounds nice, but it is fundamentally impossible.