there is a difference between self-centered and arrogant. Self-centered is actually healthy. It means you put yourself as a priority and take care of your own needs so that you are better able to meet the needs of those who depend on you. We are often taught, especially women, if you focus on yourself it is "selfish" in a bad way. The result is a lot of people who give so much of themselves away to others and to things outside of themselves they spend their lives feeling chronically drained and uninspired - just going through the motions. Those of us who put ourselves as a high priority in meaningful ways - meaning we care for our health, we do things we enjoy etc. live richer, more meaningful lives. I say this from experience - i used to be the complete opposite and couldn't understand why no matter how much I gave, I always felt empty... It's because I was going about it all wrong ;) Fulfill yourself first, and then you are overflowing and that extends out to others.
Now if you mean self-centered as in an always "me first everyone else behind me" attitude, or someone who is a classic narcissist who has no empathy for others - then no, that isn't healthy and I choose not to associate with such people.