Hi Jason. I didn't want to write equations in the post, but here is a toy example. Suppose our matched pairs consist of a boy and a girl, but we don't observe gender. Our pairs of (T, C) are then either (B, G) or (G, B). Our full sample has equal proportions of boys and girls in treatment and control and is balanced. But suppose girls attrit if they get put in control. Then we drop all (B,G) pairs, and are only left with (G, B) pairs - so the remaining pairs now have gender perfectly correlated with treatment. If gender also affects the outcome, then we no longer have a valid experiment. We would still be in trouble with a non-matched design, but would at least observe boys in both treatment and control statuses and could use bounds to deal with G attrition.