You seem to be speaking of communism, not socialism.
> The motivating force behind socialism is envy. Nobody is allowed to have something that somebody else doesn't have.
You also appear to be grossly misunderstanding motivations. The general motivation is not that existing imbalance is some sort of sin, but rather that the imbalance, by nature, slides further and further out of control.
> not for their personal gain.
Arguments about working for personal gain and accumulation of wealth mean little to working class individuals that work mostly for survival and to accumulate their employer's wealth. Individuals (especially those supporting families) living paycheck to paycheck, with no financial mobility or leverage, are surely not seeing freedom in the system or even a path to get there.