Just wanted to comment that altruism, empathy and compassion are also explainable by evolutionary selection, but that these "selfless" qualities have sometimes wrongly been excluded from definitions of social darwinism.
Yes, people tend think of these qualities as uniquely human. People like to feel unique, which makes them scarce hence valuable. You will get resistance from people explaining this, nobody wants to give up the chance to feel good about them self. Which is great for their current state of mind, but i think its bad for self growth in the long run.
But reality is of course that there is a shitload of evidence for what you said. Empathy and compassion are great traits to have for a member of a social species as humans. Knowing and understanding which other people feel is very advantageous to an individual, makes perfect sense that these traits became hardcoded in everyone during evolution.
Altruism also, but this one is a little more tricky. Natural selection does not explain explicitly why it should even exist. I heard a theory about it, dont remember the source unfortunately, which i think it has sense. Imagine a ancient group of people, everything is great, food is abundant. In this scenario altruism is great, individual does not lose much because of it, and it can gain a lot through reciprocity principle. Also, people not participating in sexual selection, it can be a number of reasons for that, can still help in the group and make it stronger as a whole. Genes for altruism get present in a greater percentage of people during this time. But imagine now shit hitting the fan, maybe a 10 000 years ice age comes up. Altruism is not so great anymore for a person. Resources are scarce, people are wasting it in sub optimal way, giving resources to people which dont directly help with their survival or their offspring's. Selfish people start to thrive, reducing percentage of people with altruistic genes during time. And so it goes, back and forth for millions of years. There is always people which are primarily altruistic, and those which are primarily selfish in a population, balance of which depends on current long term situation. When you think about it, this mechanism helps a lot in survival of the species as a whole.