Why are people brought up to believe that they have to forgive? Is it a Christian thing... forgiveness?

I don’t understand the concept of forgiveness. It is nihilistic to me. The carnal pleasure I feel from vindictiveness cannot compare to the “comfort” I feel if I rationalized something to “forgive”. If someone hurts me, why shouldn’t I hurt them? I don’t believe in god or a higher power or an afterlife, so why not have an eye for an eye before I’m too old, weak, lost or gone?