According to Jem. what are "mixed" children, and why are they sad?

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,

"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,

"...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).

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