The major reason that we're in the fix we're in is that many years ago a man named Malthus looked around and said, "There's not enough." And he made such a convincing case for it that the world economy dances to his tune to this very day. What's more, nearly every facet of our lives is informed by this idea, and we're almost totally unconscious of it. And it demonstrably wrong.
Buckminster Fuller's argument throughout most of his life was that we really do have enough, we're just being horribly inefficient about using it.
I don't think that, as it says in the Bible, "Love of money is the root of all evil", but so much of our self-worth is tied up with how financially successful we perceive ourselves to be that it might as well be true.
If money were abolished (or preferably, simply atrophied away to nothing), perhaps we would be less eager to measure other people's worth at all. If I'm not your competition or your friend or your lover, what's left? What's my role? Perhaps the mere existence of roles and our perceived need to assign other people to them is conditioned by our sense of lack and insufficiency. Perhaps the disappearance of roles would facilitate the disappearance of our defensiveness and fear and allow us to be together simply enjoying whatever is present in the moment. Imagine no longer wasting mental and emotional energy on preparation for defending ourselves against the possible hostile actions of others, actions that almost never happen even in our present world anyway.
So what has to change for a money-less world (or at least world-view) to take hold? First we need to realize our interdependency. No one can do entirely for him/herself and expect to rise above mere survival. Specialization, as we have learned throughout history, allows us to be more efficient and to emphasize quality, But a competitive economy works at cross purposes to quality. Such an economy rewards mass production of cheap products at low prices. Quality is the luxury of the rich.
If we realize our interdependency, then the next logical step is to realize the need to be in service to that. If I understand that whatever I do or produce ultimately reflects back to me, then I must create for others what I would want for myself. From a purely pragmatic point of view, if I contribute to fulfilling the needs of others, then others will want to fulfill my needs. Reputation will mean something, and quality work will be in demand. If I produce quality chairs, then soon I will not be able to keep up with demand. I will also have incentive to help upgrade the skills of lesser crafts people, and if they wish to improve the quality of their work, they will be seeking me out. Thus quality constantly increases.