Actually, it's the exact opposite.
Humans are a communal species who, if not for the arbitrary social institutions which sprang up within the last 5000 years of humanity's 120000 years on this planet that incentivize us to go against our nature, have an unending capacity for empathy and solidarity. If we didn't, we never would have formed communities to begin with.
Read Graeber, famed historical anthropologist who wrote two entire books on this very subject.