"See, how they work," the first said, "is the right lens is polarized vertically and--"

"Wait, what do you mean by 'polarized'?" said the second.

"A vertically polarized lets no horizontally polarized light in, and a horizontally polarized lens lets no vertically polarized light in," said the third. "If two perpendicularly polarized lenses are put together, no light is let through."

"So as I was saying, the right lens is polarized vertically, and the left horizontally, or vice versa, such that each eye sees a different picture."

The second had an idea. "So that means if I..." He closed his right eye, and smiled. "Yes, I can only see your right eye."

The fourth and final person (you, of course), sensed something wrong. First, you verified the second's observation. Then, you said...

You did indeed verify the second person's observation; that is, in fact you see that when you look through such glasses at another person wearing the same type of glasses, your left eye will see only the other person's right eye.  So the question is how can that be.

Note that it is only the first person's claim that the right eye's lens (really filter) is polarized vertically and the left eye's is polarized horizontally.  This is an unverified claim.

If we imagine the allowed direction as slats with a certain orientation, the glasses are made such that the right eye's filter has polarization from top-left to bottom-right as seen by the wearer, and the left eye's filter has polarization from top-right to lower-left again as seen by the wearer. To put it another way, the slants point to the upper part of the nose and the outer part of the cheeks, coming together at the top and away at the bottom.

This is symmetrical when reversed, as it would be by another person with identical glasses, so the polarization of one person's left eye is aligned with the polarization of the other person's right eye.

The same could of course be accomplished the opposite way: the polarized "slats" pointing to the bottom of the wearer's nose and the top-outer part of the person's temples.  But I think real 3-D glasses (of the polarized kind, rather than the red-green), are made in the way I originally described (top-in to bottom-out).