Nowhere identical when reversed.
The opposite to

symmetric.

Another opposite to 'symmetric' is
asymmetric, which merely means
'not identical when reversed'.

In mathematical terms: a relation R is asymmetric if E.x: x R y ^ ~(y R x);
it is antisymmetric if A.x,y: x R y => ~ (y R x).

I wish Everything was case sensitive and LaTeX aware.