why does any partially ordered need to be antisymmetric?
why can't there be 2 elements in a poset with different values but order-wise have the same order priority? what's the motivation for this?
Does it even make sense to think of order without antisymmetry?
The answer seems to be that in any pre-order you can define an equivalence relation where two elements are equivalent if each is related to the other. When you mod out by the equivalence relation you get antisymmetry. In many applications the antisymmetry is important, but in some others not. That is why you have pre-orders and stronger orders. If the order has the stronger property it makes sense to acknowledge it.