When I look, I see that I have no option but to function in a self-centered way.
As long as there is a belief in the idea of I, that functions as a center in my world. Whatever this idea of I is placed on (my human self, family, nation, Earth, life, universe, witness) become the center of my experience and functioning in the world. Whatever I do, however selfish or altruistic it may seem from a conventional view, is for myself.
I act from a should. I act from a belief. I act from a sense of ethics. I act from my integrity. I act from a sense of compassion. I act from a realization of interconnections. And so on. It is all for me, although I am of course free to tell myself the story that I am doing it for others.
And when this belief in the idea of I falls away, when there is a realization of selflessness, we can say that the self-centeredness also falls away. But we can also say that it just changes from self-centeredness to Self-centeredness. The new center (of gravity) is in Big Mind, the realization of Ground. That which has center nowhere and everywhere, and yet is temporarily functionally centered on a particular human self.