It is impossible to achieve Socialism

In general, all system builders (Plato, Aristotle, Hegel and Marx) that lead to the conception of Socialism believed that our society is progressively moving from imperfect to perfect. They assumed that mankind is going to simultaneously achieved ethical and logical perfection.

Even if we consider heredity and survival of the fittest, centuries of interbreeding between "acceptable perfect human" (by the current definition of that time) will not guarantee an equal race. There would still be people that are going to be smarter, bigger and/or stealthier that can destroy a seemingly classless society. There are still people who are going to be natural leaders and people that are natural followers.

Collective ownership of everything implemented since birth wouldn't also guarantee that people will grow up to just accept it. Bending of personalities and traits always results to resistance. As long as the human mind can perceive that it is being persecuted and see itself as a victim, struggle will ensue.