Not the case by far, Research the following Altruism in animals.
There were studies done in the 50's/60's on RATS, the rats were put one to a full metal wire cage, and one of the two rats would have a lever that once pressed it would release food but also electrocute the other rat. The rats would starve rather than cause harm. So much for "we are selfish", there's plenty of evidence of empathy in all kinds of creatures, this is natural, this is reality, the whole bullshit argument that we are selfish flies in the face of what most people exemplify, completely.
I will try to look for that experiment if you think it is a good example. But also try to think about some points!
-How was it possible that some partially civilized evovled apes are putting RATS into cages just to check their altruism ?.
-In 1974 a really interesting book was published Egoistic Gene by Richard Dawkins. I would advise you read it if you have the time, it explains a lot about altruism and our species.
-I think you missed the point of my comment, which I believe lies in the last lines of it
Have a good day!