Two of my friends gave me an answer to the original question.
Moshe G. answered that looking at the time-reversed picture shows that the magnetization in both directions MUST BE THE SAME (when the direction of time is reversed, the directions of the magnetic field and the magnetization are reversed, while the crystal remains unchanged; and it is known that the relevant laws of physics are symmetric in time).
Vadim K. answered that looking at the mirror reflection, with the mirror perpendicular to the line of atoms, also shows that the magnetization in both directions MUST BE THE SAME (in the mirror, the direction of the crystal is reversed, but the magnetic field and the magnetization keep their directions; and it is known that the relevant laws of physics are symmetric under mirror reflection).
I added then that if the mirror is parallel to the line of atoms, it also proves this statement in a similar way.
So simple!
[banana]