请教一道语法题：

1.       A recent New York Times editorial criticized the city’s election board for, first of all, failing to replace outmoded voting machines prone to breakdowns, and secondarily, for their failure to investigate allegations of corruption involving board members.

(A) secondarily, for their failure to

(B) secondly, for their failure to

(C) secondly, that they failed and did not

(D) second, that they failed to（E）

(E) second, for failing to

答案是E，但是second不是形容词吗，这里看着应该放一个副词与first of all 对应啊，确实按照堆成来说for failing to没有问题，但是我比较纠结为什么是second，不是secondly

非常感谢