the doctrine was generally abandoned in favor of the opposing view= the doctrine was generally abandoned to support the opposing view.
因此in favour of 可以看作状语,表示目的。
Although qualitative variance among nerve energies was never rigidly disproved, the doctrine was generally abandoned in favor of the opposing view, namely, that nerve impulses are essentially homogeneous in quality and are transmitted as “common currency” throughout the nervous system.
这里in favor of是什么成分,总是觉得和前面的句子格格不入。特别像动词而不是状语。