Although this question got a clear and accepted answer.
I would just like to share with readers that the word 'transitive' here is used with reference to a mathematical (logical) property 'transitivity'.
Transitivity means that a relation between three elements is such that if it holds between the first and second and it also holds between the second and third it must necessarily hold between the first and third.
For example; if A is larger then B and B is larger than C; then we can say Ais larger than C.
So, as @Max S. has described; "Two-way preferences need not be transitive." means that
"The first classifier pair says 'prefer c2 over c1' the second classifier says 'prefer c3 over c2'. If the two-way preferences were transitive you would expect the final classifier to say 'prefer c3 over c1', but it doesn't, that classifier prefers c1 over c3!"