"Everyone for himself and the devil take the hindmost"---what does this really mean?

You really think that people should be selfish? I learnt from a enlightened sage says that, when we help others, when we are doing good deeds, we feel good in our heart, so we are for ourselves. If we think of evil things, and do harm to others, we also feel the evilness and harm in us, we are hurting ourselves. In this way, “Everyone for himself” means be good to ourselves by means of taking care of others and well treat others. Do you agree? 😀