Because if you just add one element to the set it no longer has the property, and hence the predicate is not monotone. In more detail ... He's talking about p

Because if you just add one element to the set it no longer has the property, and hence the predicate is not monotone. In more detail ... He's talking about properties (or predicates) that are monotone. That means that if P(S) is true, and T contains S, then P(T) must also be true. But when P(X) is true if and only if X has an even number of elements, then P({a,b}) would be true, but P({a,b,c}) will not be true. Then P would not be monotone.