Why is it necessary to express the group of criterion as an array?

This works just as effectively.

=SUMIFS(A:A,N:N,"<>"&1,N:N,"<>"&2,N:N,"<>"&3,N:N,"<>"&4,N:N,"<>"&5,N:N,"<>"&6)

If you do require the use of a nested array, you may wish to use SUMPRODUCT instead.