Do you think friendship isn’t about gaining or about expecting more that what we need, but to love, give happily and forget?

Recently, I’ve read this quote in a book and I’ve been wondering if this is the right thing to do. Im a pretty strict person when it comes to people because i don’t allow myself to trust, so when they make a mistake i cut them off. Maybe that’s selfish, or maybe the world is in fact cruel. What do you think?