There are many definitions of ego. The one we use here is consistent with Eastern spiritual traditions, rather than modern psychological usage. Such spiritual doctrines say the ego is a concept, an idea about who we are. Most precisely it is this idea: "I am a separate and vulnerable person."
People we call egocentric almost surely subscribe to this idea. But so do the rest of us. It is well known that egocentric behaviors are efforts to compensate for inadequate self-image. We are all egocentric in that we feel our selves to be inadequate: we just have different ways of trying to compensate for it. This definition of egotism includes all behaviors motivated by the ego-concept. Even shy people, even self-effacing people -- all kinds of people, in fact -- are being egotistical in this sense.
The problem is, as long as we have the ego idea, we have the desires that go along with that idea. What does the ego want? The ego's desire is to keep you safe by keeping you separated. The ego wants you to think that life without love is the only safe way to go. It wants you to run away in fear from present involvement, believing closeness might tear you limb from limb! In short, it would turn you off about giving, receiving, committing, opening up, and sharing -- all the things that love depends upon.