Is there a physical interpretation of the alternating property? A map from lists to list-elements is called "alternating" if any list with repeated elements is mapped to zero.
This has statistical significance: regressions on collinear data are bad, dependent columns add no information, etc.
But alternating maps like determinants and wedge products show up in physics as well. Is there an intuition to go along with the skew symmetry and alternatingness in that domain?

The oriented volume spanned by three vectors is a multilinear alternating map of the vectors themselves. That's the starting point.
See, e.g., the book by S.Winitzki.
