My source is from etymonline . com and the key words searched are demon, tide, and monos. Demon can be seen as a form of the word daimon , though I wanted to look past that and came up with the Grecian word demos (meaning people) which has the PIE root of da- and mono , which is seen as separation/division or group of individuals and singular/alone/one, respectively.
From this, we can see da-mon as the separation of a singular whole, or in reference as to the saying of 'the sum all parts' where demos relates specifically to the parts. We can honor that we are part of a larger picture while still being able to recognize that we are indeed individuals.
When thinking of the spirits we call demons, most call up the image of Hell, damnation, and evil personified. However, those who work with demons recognize that an entire race of beings cannot be identified with a singular traits as they are all individuals with their own personalities (as was just demonstrated in the etymological research). I could go on about how this could be interpreted for hours, but I shall leave it up to the reader to meditate on.