The ethical and practical rationale for socialism can be explained very clearly through game theory. Consider the two most famous game theory scenarios, the Prisoner's Dilemma and the Ultimation Game.
Prisoner's Dilemma: Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar deal—if one testifies against his partner (defects/betrays), and the other remains silent (cooperates/assists), the betrayer goes free and the cooperator receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept quiet. What should they do?
In the absence of a social contract, the decision is easy: each prisoner should attempt to betray the other. Afterall, if the other remains silent, they walk away free, while if the other cooperates, it is better to get the three month sentence for betraying each other than to have all the blame pinned on you. Thus, in purely rational terms it is best for each prisoner to attempt to betray each other, each ending up with three months in prison. There is, however, a better scenario for both - both remain silent and both only serve one month in prison. This is the win-win scenario, but it requires a social contract, an implicit assumption that the other will behave in the same manner. Many variants of the Prisoner's Dilemma or the related Hawk-Dove game exist, and the mathematically-proven optimal scenario is to have a social contract that each individual will accept a minor loss and not pursue maximal gain. Furthermore, the social contract works best when it is enforced by a neutral third party, with the capacity to punish cheaters. In essence, this is what government is, a neutral third party created to enforce the social contract. We all make minor concessions (pay taxes, agree to drive on the same side of the road, etc) and in return we live in a much better society than if everyone tried to cheat off others.
This is probably the rationale for the rise of religion - as an enforcer of social contracts, religion would create some of the gains that come from solving the Prisoner's Dilemma. Better, of course, is a system that is more inclusive (ideally, everyone in a society) and that each individual has some say over what social norms are enforced i.e., a democratic government. So apologies to any anarchists or liberitarians, but government is in fact a distinct advantage to individuals. But why does this lead to socialism? Afterall, a government that enforced a social contract of pure capitalism would equally solve the Prisoner's Dilemma.
Here we need to consider an second game, the Ultimatum Game.
Ultimatium Game: Take two people and tell them they have the opportunity to split $10. Furthermore, tell one person that, as first mover, they get to make a one time offer, and tell the other person that, as second mover, they get the opportunity to either accept or reject this offer. If the offer is rejected they both go home with zero. If the offer is accepted, they each walk away with the proposed split.
Game theorists and capitalists agree, the solution is easy. The first person should offer the smallest possible amount (1c) and the second person should accept it. Afterall, why would the first person give away any more of their wealth than required to make the deal accepted? And the second person should accept it, since 1c is better than nothing.
Fortunately, the capitalists are completely wrong in every experimental test of the Ultimatium Game. The Game has been run in many formats in many cultures all around the world, and the "solution" never occurs. Firstly, most people when making the offer tend to propose ~50%, giving away far more than the pure capitalist or game theorist would. Secondly, most people receiving offers will reject any offers below 25%, preferring to have everyone walk away with nothing rather than let the first person have three times more than themselves. Amazingly, this is even true when the unfair portion is equal to two weeks wages. People have an innate and viseral disgust at inequality. The Ultimatium Game teaches us that people are happier accepting $5 each from $10, than they are in accepting $10 from a $100 split.
This is why socialism. We need government to enforce social contracts that make us all better off. We need democratic governments to create social contracts that benefit the majority of people. And we need socialism because our humanity is based on an intrinsic desire for equality. Pure capitalists will talk about "growing the pie" so that your tiny piece is a little bit bigger, as if we are all pure rationalists that would accept the 1c offer. But we are not. Socialism is about making the social compact a 50% offer, rather than the minimal 1c offer. Socialism is the statement that equality has value above and beyond what your share is. Equality gives value to our lives, makes us happier and healthier, and is aligned with the basic human instinct.