spect: derived from Latin "specere", meaning "look"
-ive: of doing something
So respective means:
Of looking to the first direction, and again to the second, and again to the third...
It indicates "referring to every single direction, aspect, or person".
Evolution of usage
You all, of being looked from the first direction, and again from the second, and again from the third..., need to write a report to me.
You all, of all respects, need to write a report to me.
You all, respectively, need to write a report to me.