What makes a "mixed child...real sad" in To Kill a Mockingbird? What does this tell you about society?

According to Jem, a "mixed child" - one who is "half
white, half colored" - is "real sad" because they do not belong anywhere. Jem astutely
explains,

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"colored folks won't have 'em because they're
half white; white folks won't have 'em 'cause they're colored, so they're just
in-betweens, don't belong
anywhere."

This observation
expresses the virulent racism that permeates southern society at that time. A person is
classified and judged by the color of his or her skin, and it works both ways, with a
black child unable to be accepted in white society, and a white child unable to be
accepted in black society. The lines delineating the racial divide are unyielding; they
are a fact of life, and are difficult, if not impossible, to
breach.

The racism that Jem describes actually goes beyond
skin color. Scout notes that one of the mixed-race Raymond children looks no different
than a child who is all-black, and Jem tells her that "you just hafta know who they
are." Jem says,

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"...around here once you have a drop of Negro
blood, that makes you all
black."

If it is known that a
person has even one person of Negro ancestry in his or her lineage, that person is
condemned to live in the netherland of the "mixed child;" belonging
nowhere.

Jem hints that the racism and strict divisions
along color lines are lessening in other areas beyond the Deep South. Mr. Raymond has
sent two of his children up north, where "they don't mind [mixed children]" as much
(Chapter 16).