Selfishness includes greed and aversion. When we have aversion to the world, we want it to be the way we want. We are considering me, myself, I. Greed and aversion can both come out of selfishness. I want this or that, I don't want this or that. So there is still an "I want." One, we are grabbing for, or one, we are pushing away.
So when we are selfish, we are doing both. Now, you know selfishness itself covers so much, that working with your desires, your greed, your aversions and so on, you don't really have to bring in so much the thought of selfishness. It's just obvious if it's creating Dukkha. If you see the Dukkha of greed, if you see the Dukkha of aversion and if you bring forth the Compassion you want to end the Dukkha, then the minute you bring forth the Compassion, the selfishness changes over to into selflessness. You are only thinking of ending pain. That's very different to wanting something or wanting something go away, just to satisfy me. But to become selfless is a compassionate motivation, wishing to end pain.
And when a person becomes selfless it doesn't matter whether it's their pain they are trying to end, or someone else's pain they are trying to end. They just start becoming aware of Dukkha everywhere they see it. Inside or outside, it doesn't matter anymore when a person is very selfless. When a person is very selfish, everything centers around the self. That's basically the definition. Selfishness means, me, my world is most important. Or, I want, I'm going to get, nobody else matters, I'm the only one who's important. But the minute we become selfless, then we are not anymore important in that sense compared to other people. If we can end someone else's Dukkha, we try to. Because ending Dukkha becomes more important no matter if it's inward or outward, than just me having my own happiness.