most teachers say to use the 50mm because it close to what the human eye sees.
Incorrect. The human eye perceives a very wide field-of-view. Look straight ahead and then focus on the view around yourself; note how you can see almost a full 180º horizontally. The retina covers a whole lot of the back of the eye, save for the blind-spot where the ocular nerve connects to it. These outer edges are extremely blurry, lack detail, and are monochromatic (your brain can fool you though, if something with a continuous tone is extending from your sharpest field-of-view into this area by filling it in with approximate colour).
The fovea, on the other hand, has an extremely narrow angle of view; about 2º from centre, or a dime held at arm's length. This area is packed with colour-sensitive cones (there are three types, one each for red, green, and blue, though we have mostly green, then red, then blue photoreceptors). The fovea also has some rods, but they are vastly outnumbered by cones. This is your sharpest angle of view; a paltry 2º. You hit the blind spot on the interior side (side closest to the nose) at approximately 10º. Visual acuity has already dropped almost three-fold by this point.
See here for a graph.
Coming back to lenses and how all this shapes-up next to lenses. The first thing to keep in mind is that the eye is essentially circular; a sensor is rectangular. So while the diagonal, vertical, and horizontal angles of view are the same for the eye, they differ on a camera depending on the sensor's dimensions and size.
The fovea, at a mere 2º angle of view, is roughly equivalent to the angle of view of a very long telephoto lens. A 35mm sensor is 36mmx25mm, making the diagonal roughly 43.3mm. Then we do a quick calculation (I just know the approximate focal length off-hand; it's 600mm): angle-of-view = 2arctan(43.3/2(600)). The angle of view comes-out to around 2º, with a little rounding in there for my own sake (I don't have a scientific calculator).
So your
sharpest angle of view, the fovea, is actually equivalent to the angle of view of a 600mm lens on a 35mm sensor. Doing the above calculation again, for a 50mm lens, we find that the diagonal angle of view is actually around 49º. That's sure far away from our 2º fovea. If you look at the above graph again, you'll see that our visual acuity at an angle of 49º is just so paltry as to be practically useless for anything beyond detecting fast motion.
This entire 50mm = human eye thing is a misnomer.
As for compression of field (by this I mean how relative distances from the camera lens effects how such objects are rendered on the sensor or film; wide-angle lenses produce images where what is a little closer to the lens is much larger, yadda yadda), 50mm on a 35mm sensor is pretty nice; no wide-angle-like distortion, no obvious compression. It's for that reason that I can understand how people come to see this focal length as close to what the eye sees, but that point is moot as well when one considers how the human brain interprets the information from both eyes. We compensate a lot for the wonky distortions that we see with wide-angle and telephoto focal lengths. You can see a little of this if you close an eye and look at something up close; you've removed the brain's ability to use binocular cues to interpret what you're seeing better. Though, even then the eye and brain do a great job at not messing things up (the fact that the eye is physically smaller than a camera lens, and your retina smaller than a 35mm sensor, has quite a bit to do with it). Pretty cool piece of biology, the eye.
