How does 斡旋 mean "to mediate"?

Question

I'm studying CCTV news with my Chinese teacher, where I encountered the word 斡旋 for the first time:

CC-CEDICT: 斡旋 (wò​xuán​) to mediate (a conflict etc)

CC-CEDICT: 斡 (wò​) to turn
CC-CEDICT: 旋 (​xuán​) to revolve / a loop / a circle

I'm familiar with words containing 旋, like 盘旋 = "to spiral" and 旋涡 = "whirlpool". My 现代汉语词典 dictionary suggests 斡 is largely only used in the word 斡旋. I didn't find anything useful on Dong Chinese aside from 斡 being a rather rare character.

I'm fairly sure I'll forget this word in about 10 minutes time. In any case, it'd help me remember if I understood the underlying logic: currently it doesn't seem to make much sense "to turn" + "to revolve" = "to mediate".

Question: How does 斡旋 mean "to mediate"?

Answer 1

The subject to be "mediated" is naturally "conflict"

To turn and revolve around (the conflicted parties) = to mediate (the conflict)

Example:

为中美贸易冲突斡旋 - Mediating the US-China trade conflict

The mediator has to go back and forth between the Chinese and the American government to Mediate the conflict

Answer 2

Nowadays this is a rather official word used in situations between two countries. Actually, it is rarely used. People using it may just show that they were well educated. Anyway, I think it's OK that you just forget it.