"Suppose that two features $[x,y]$ from a population $P$ are positively correlated, and we divide $P$ into two subclasses $P_1$, $P_2$. Then, it cannot happen that the respective features ( $[x_1,y1]$ and $[x_2,y_2]$) are negatively correlated in both subclasses
Or more succintly:
"Mixing preserves the correlation sign."
This seems very plausible - almost obvious. But it's false - see Simpon's paradox