I'm not the one to teach you. But for starters, I'd say to begin with the recognition that there are all kinds because everyone comes at problems from different angles.
Philosophical anthropology is perhaps one such angle, and certain traditions give as the fundamental distinction between body and soul to be characteristically human. The Greek tradition.
But this body soul thing is not cosmological. So there are others. Logical ones? A is a and not non-A. This yields the principle of non-contradiction formalized by Aristotle. The old and new man? That is the Pauline distinction in the doctrine of creation. I'm sure to be missing many more.
I sometimes use the term "dualist" to designate those who recognize a distinction and then favor one at the expense of the other. They hop around on one leg and claim everyone else has only one too. Or that the other leg was no use anyhow. They make very poor dancers. They can also be very tricky and grow back their other leg but lose the one they had.
And so I think Dooyeweerd is right that dualisms often resolve on one side or the other or embark on an interminable struggle. Then comes the yin & yang types that make the struggle the fundamental cycle and arche of all and everything. Dr. Erixymachis in Plato's Symposium tried that trick.
I don't know why we are so disposed to it. The Greeks are to blame, according to many. But even Aristotle made an important point in his ethics. Virtue is a mean, but not a mathematical mean, as if you could take 1 mol of excess fear and add to it one 1 mol excess recklessness to arrive at courage. No, he said the virtues are not a balance of extremes, but a mean relative to us. So Aristotle, as much as he was dualistic in describing the human person as a form-matter complex (body-soul, if you will, but not Platonic; Socrates said it was an entombment but a harmony). For virtue he sought the ordered relation of part to whole and the ordered relation of actions to an end.
Human frame of reference fallacy
____________________________________________________________________________
And the same dualism is dealt with more fully here... this is looking pretty good, too:
Dueling with Dualism
Nancy Scott
http://www.mckenziestudycenter.org/philosophy/articles/dualism.html
____________________________________________________________________________
And for a further flung look into various kinds of dualisms out there:
Dualistic Discourse
Strong emphasis on two forces at work in the world
Darren Witwer
http://www.mctc.mnscu.edu/~witwerda.faculty/religions/dualism.htm
____________________________________________________________________________
And here's about the common, current (or do you say post-modern? --maybe if you're in a really big hurry you do;-) dualism that betty boop referred to:
THEOLOGY AND SCIENCE WITHOUT DUALISM
Elizabeth Newman
http://www.aril.org/newman.htm
Only to a non-Christian. The problem occurred when the then self-appointed universal church (Roman Catholicism) decided to adopt Aristotlean views of the cosmos, which was just one single spoke of many in the wheel of corruption of the Church of God.