Basically, I'm asking if anyone knows of a possible etymological reason. Maybe it has to do with the ideogram itself, maybe it's a saying, but I'm not finding satisfying answers online.
Apparently, in Chinese it can also mean "in an awkward or difficult position", and according to wikitionary entry for the chinese etymology of the word:
An Old Chinese ideophone of the phonetic shape /raːd(s) paːd(s) ~ raːŋ paːd(s)/ (ZS), initially used to describe a limping or stumbling gait. Folk etymology (as used by Tang-Dynasty Duan Chengshi) states that 狽／狈 (bèi) was a wolf-like animal in Chinese mythology, which had very short forelegs and long hind legs, and needed to mount a wolf in order to walk, so the two animals would always hunt together. This eventually led to the meaning of “to conspire”.
I can see how this would lead to the meaning of "being in an awkard or difficult position". Further, the ideograms being two different kind of wolf kanji also make sense with this etymology, given that one wolf rides the other, and one is a legendary kind of wolf.
But then again, that's the Chinese etymology/meaning, and I'm more interested in the Japanese one. Apparently, 狼狽する is also in the phrase 周章狼狽する, which also means "consternation, falling into panic". And according to this answer on Japanese Yahoo Answers, it has to do with the codependence of both of the wolves, and it later changed, but there's no source on that.