Confusion around rotation of Graphics3D objects

Question

Subject says it all: I don't seem to be understanding how Mathematica's functions for rotating 3D objects work. Below is a simple example: What I want to do is rotate the cube in the example around an axis normal to the view vector through the center of the cube. What I expect to see is a "spinning" cube, at a fixed position and size. Here is my code:

cgxt[t_] := 
  Graphics3D[Rotate[{EdgeForm[], 
             Hue[30,100,100],               
             Cuboid[{1,1,1} - 1/2, {1,1,1} + 1/2]}, 
             -t Degree, {1, -1, 0}, {1, 1, 1}], 
             Lighting -> {{"Ambient", RGBColor[0.7, 0.7, 0.7]},
                          {"Directional", RGBColor[0.7, 0.7, 0.7],             
             ImageScaled[{0, 5, 0}]}}, Boxed -> False];

which I then demonstrate with

Manipulate[Show[cgxt[t], ViewPoint -> {1000, 1000, 1000}], {t, 0, 180}]

This does not have the desired effect: It looks like the cube is rotated around some off-center axis, changing size as it does so. Interestingly, this effect does not seem to change if I change the location of my cube or the location of the rotation axis independently.

Can someone explain to me what I am missing?

Note (added after discussion below): The following function works as expected, but it's still unclear to me why Mathematica does what it does.

cgxt2[t_] := 
      Graphics3D[Rotate[{EdgeForm[], 
                 Hue[30,100,100],               
                 Cuboid[{1,1,1} - 1/2, {1,1,1} + 1/2]}, 
                 -t Degree, {1, -1, 0}, {1, 1, 1}], 
                 Lighting -> {{"Ambient", RGBColor[0.7, 0.7, 0.7]},
                              {"Directional", RGBColor[0.7, 0.7, 0.7],             
                 ImageScaled[{0, 5, 0}]}}, Boxed -> False, 
                 PlotRange -> 2 size {{-1, 1}, {-1, 1}, {-1, 1}}];

Answer 1

cgxt[t_] := With[
   {
    viewpoint = {1000, 1000, 1000},
    center = {1, 1, 1},
    size = 1,
    rotvec = {1, -1, 0}
    },
   Graphics3D[
    Rotate[
     {
      EdgeForm[],
      Hue[30, 100, 100],
      Cuboid[
       Sequence @@ Outer[Plus, {1, -1} size/2, center]
       ]
      }
     , -t Degree
     , rotvec
     , center
     ]
    , Lighting -> {
      {"Ambient", RGBColor[0.7, 0.7, 0.7]},
      {"Directional", RGBColor[0.7, 0.7, 0.7], ImageScaled[{0, 5, 0}]}
      }
    , Boxed -> False
    , ViewPoint -> viewpoint
    , PlotRange -> center + 1.5 size {{-1, 1}, {-1, 1}, {-1, 1}}
    ]
   ];

Manipulate[
 cgxt[t]
 , {t, 0, 180}
 ]