Why are points of zero Gaussian curvature called parabolic? The sign of the Gaussian curvature can be used to classify points as elliptic, hyperbolic, and parabolic. Wikipedia has this image with example surfaces:

I see how a hyperboloid surface has hyperbolic points, and respectively a sphere or ellipsoid has elliptic points. So these are aptly named.
But why are points with zero Gaussian curvature named parabolic, not something like cylindrical or conical?
Especially, a paraboloid has positive curvature.


Nomenclature is from origin of conics categorization . Among the conics  eccentricity $\epsilon$ for a hyperbola, parabola and ellipse are $ \gt 1, = 1, \lt 1 $ respectively. In its categorizing work sign of double or Gauss curvature relates to $ (1- \epsilon). $
In the equation of conic( two dimensions) there is already an indicator of things to come when it would be embedded in 3-space.   For $ a x^2 + 2 h x y + by^2 $ + linear  terms =0, then the sign of invariant $ a \cdot b - h^2 $ also decides to which of the three types the conic under consideration belongs.
Accordingly in $ \mathbb R^{2}$ say for a surface in Monge form $ z= f(x,y), K= (r \cdot t - s^2)/(1+p^2+q^2)^2 $ (partial derivatives of z) decides sign of Gauss curvature K, i.e., to which of the three types you have shown the surface belongs.
EDIT 1:
Also if a reputed mathematician had called it that way and it stuck,the matter of distinguishing between the three was settled temporarily.
Having said the above in defense of what I believe is the staus quo ante I am in agreement with the OP about inappropriateness of the parabolic appellation of $ K=0 $ flat surfaces.
When a paraboloid  is and quite apparently looks $K >0$ there is no need to cling on to any historical reasons. In line with the view of OP  I too like to see it changed to  developable or  flat, but not further retain  parabolic. 
