Why do some people prefer the following axiom (e.g. deFinetti)
If $A,B \in \mathcal{B}$ where $\mathcal{B}$ is a $\sigma$-algebra of sets and $A,B$ are disjoint then $P(A \cup B) = P(A)+P(B)$
over the following
Suppose $A_1, A_2 ,\dots \in \mathcal{B}$ and are pairwise disjoint. Then $P \left(\bigcup_{i=1}^{\infty} A_i \right) = \sum_{i=1}^{\infty} P(A_i)$