The Sibling Paradox

Seems like a title for a The Big Bang Theory episode (excellent TV show), but this refers to the geometric contradiction found in most families, i.e., no matter how many kids there are, they will all be opposite from each other.  This goes beyond the psychological explanation that younger kids will find areas of expertise different from their older siblings in order to not compete directly with them, that children will receive different amounts and types of attention based on birth order effects, etc.  No, the geometric impossibility of all children being opposites can be commonly observed (just look at your own siblings or children) even when children are just infants and toddlers.  Why children with such similar genetics can almost invariably have personalities so different from each other is a great mystery.  And then each child grows up and finds yet another opposite to marry.