Escroda and 11ant rather do not like the asymmetrical roof.
You know more about that than I do.
I would consider a skew-hipped roof not exactly wrong to call "asymmetrical," but I associate an asymmetrical roof more with equal eaves height and unequal slope (in my opinion fully retro, that was considered highly avant-garde in the 60s and stylish in the 80s) than with what is intended here (by the development plan issuer): unequal eaves height but symmetrical slope.
I can also come to terms with asymmetry, my husband is a bit more reserved about it.
There is absolute and relative symmetry, i.e. you can look at it from the perspective of the vertical axis, then the roof with different eaves heights is always "skewed"; or you relate it to the slope of the terrain – then it is
not skewed if the relative eaves height above ground level is equal and the ridge is orthogonal over the imagined baseline. Almost like with blondes: "left" is just "the other right".
Perhaps that was the case here when the municipal council discussed the development plan: the majority faction preferred the latter explained view of symmetry.