Wouldn't everyone have to be altruistic for socialism to work?

No. Socialism isn't based upon altruism. Socialism will work even if everyone suddenly decides that they dislike everyone else. Supporting socialism involves recognizing the fact that the current system just doesn't work for most people. Socialism will be a society in which satisfying an individual's self interest is the result of satisfying everyone's needs. It is enlightened self-interest that will work for the majority.