When my wife and I can't decide what we want for dinner, we use a sort of game to decide.
"Hot or cold?"
"Eastern or Western?"
"Spicy or not?"
And so on. Yes, it's an obvious oversimplification of how food works. It's a construct used to help us decide what we want for dinner - to help us get from point A (hungry) to point B (not hungry). The universe, like food, comes in many different flavors. But using dichotomy helps us make sense of those flavors, to sort them and keep them from becoming overwhelming.
After that first duality comes what you might think of as yin and yang, darkness and light, or, as deities, the Wiccan God and Goddess, or Waincraft's Star-Mother and Shaman-Father, or Izanagi and Izanami, or any other original pair. This binary differs from the first in that they are both extant - both exist, there is no question of non-being here. Instead, the question is what kind of being they are. I don't think I can say much more about this than I did in last month's post on Yin and Yang.
For me, this primary dichotomy is the firebird and the dragon, or the serpent and the eagle. Two powers in opposition - one of air and fire, the other of earth and water, they exist to compliment and to contrast with each other. This is the dichotomy of first principles; everything else flows from this. (I think the original binary is to broad and basic to really be considered a first principle.) Conflict and harmony both arise from the first principles, as do creation and destruction, as do the elements. Everything starts in that first awareness that there is self and there is other.