Why are the axis labelled as such in the 3d Cartesian coordinate system?

Question

A long time ago I was taught that in 3d space, the x axis is the length/width or left/right space, the y axis is the height, and the z axis is the depth.

When we draw things in 2d on a page, this seems consistent for x and y:

y
 |
 |
 |
 |________
           x

Now we have a 3 dimensional grid:

   (y)
    |
    |
    |
    |________
   /          (x)
  /
 /
(z)

Intuitively, I'd "overlay" the 2d grid over this, so the x would be going from left to right, and the y would be going up and down. z would be the axis extending into and out of the page, which makes sense because that's depth. This seems very consistent

Then why do we label the axis like:

   z
    |
    |
    |
    |________
   /          y
  /
 /
x

Where did this orientation come from? y is where x used to be, and z is where y used to be. The only "artifact" from 2d is that the positive y axis is 90 degrees counterclockwise from the positive x axis. Where is the consistency? Surely there's some mathematical reasoning behind this? We didn't just cobble it all up to mess with students?

On a side note, the video game Minecraft labels the axis the way I thought would make sense (y up/down, x east/west, z north/south), although it makes z+ south and z- north.

Answer 1

In physics, the orientation of the 3D plane is very important. The second way how you graphed it, obeys the Right Hand Rule, an important rule in electricity. In this manner, the force is pointing in the positive direction of z

Answer 2

Comment

For a surface of revolution using cylindrical coords and helices one would llke to keep the right hand side going arrow positive as symmetry axis, still sticking to familar cartesian $(y,x)$ going up and out of the page in the RH system intact. So it depends upon the overall object situation in reference also.