Maybe this helps to wrap your head arround:
Ok you want to match the 3D-object (model) with a 2D-object (texture).
Taking a cigarrette-box as an example you would do this by cutting edges and unfolding
until the 3D-object is in 2D-space.
(ok, you don`t do it really, just for visualizing the concept)
Regarding the artifact on your model, as already mentioned, is due to
the texture-space available for this model. Visualized with the red bar
it is obvious that the space does not match proportional with the given
2d-space. Therefore the fewer pixels will be stretched across the surface.
(Or like in your case 1 pixel will be stretched all across the front side of your cabinet