Full Idea
The axiom of choice was an assumption that implicitly questioned the necessity of intensions to guarantee the presence of classes.
Clarification
'Intensions' here are concepts which generate the classes
Gist of Idea
Choice suggests that intensions are not needed to ensure classes
Source
J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'Log')
Book Reference
Coffa,J.Alberto: 'The Semantic Tradition from Kant to Carnap' [CUP 1993], p.114
A Reaction
The point is that Choice just picks out members for no particular reason. So classes, it seems, don't need a reason to exist.