In the yin-yang dynamic, yang is pretty much always the dominant force: it represents the sun (the "great yang", 太陽), brightness, positivity (陽性), masculinity (the penis, 陽物), the living (陽間, 陽世), etc. Yin on the other hand, represents the moon (the "great yin", 太陰), darkness, negativity (陰性), femininity (the vagina, 陰物), the dead (陰間, 陰府), etc.
So why does "yin" comes first in the compound "yin-yang"? If there's "south-north" (南北), in which case south is more yang and north is more yin, why isn't there "yang-yin"? Was there some phonotactic restriction that prevented yang from coming first in Old Chinese (like say, certain sounds are forbidden to appear before certain sounds)? Or is it about some phonetic harmony that makes "yin-yang" sound better than "yang-yin"? I suspect that given the Middle Chinese reconstructions of both elements (something like /ʔim/ and /jaŋ/), it probably didn't sound great to have the /ŋ/ in "yang" in front of the vowel or semivowel in "yin".