I don't have my full array of dictionaries at hand, but the Oxford Latin dictionary (the only one worth considering in my opinion if you want a serious discussion) gives the etymology of scio (the root verb) as possibly related to Sanskrit chyati and Greek schizo (as in schizo-phrenia, actually), both meaning to separate. I can't say for the Germanic connection to shit and friends, but it's not impossible, although I'm not sure where the l comes from.
I'm not entirely sure which root the Sanskrit form should be but it might be chid-, which fits with the Greek. In that case, I'd wager an Indo-European root along the lines of skedH-, with palatal k and laryngeal (IIRC, it's the laryngeal that gives the Greek z).
As for the derivation of the meaning, I think the notion of "separating right from wrong" is reasonable, but these things are often notoriously hard to pin down.
I'm not entirely sure which root the Sanskrit form should be but it might be chid-, which fits with the Greek. In that case, I'd wager an Indo-European root along the lines of skedH-, with palatal k and laryngeal (IIRC, it's the laryngeal that gives the Greek z).
As for the derivation of the meaning, I think the notion of "separating right from wrong" is reasonable, but these things are often notoriously hard to pin down.