i) Since the snake was seen at some point of time gives it a positive nature during that time.
ii) Since it disappears after knowing it to be a rope gives it a negative nature not only after knowing the rope to be a rope, but also the same person will not see, and not be able to see, the snake again even if he wishes to and can not be scared by it after knowing the rope!
iii) But since it was a snake *once*, even while being a rope, gives an apparent reality to the snake from an unbiased neutral analysis. How the snake made its first appearance cannot be known, beyond the absence of knowledge of rope. So the "when?" or time factor of avidyA formation also becomes a moot point! A question if posed to the person in (i) as to "since when do you see the snake?" will amount to a reply "since ever". So avidyA is said to be anAdi, without a beginning, or to mean untraceable beginning, inexplicable, indescribable or anirvachaniya.
To my understanding, Shankara left the description of jagat as mithyA (apparent reality, not illusion) and didn't describe it further is for this reason, since it cannot be described. Logic falls short of understanding timelessness of anything; we are tuned to think in finite dimensions, avoiding ad infinitum.
If you ask a person who doesn't know German since when does he not know German, what kind of answer do you expect? Similar is the case here. But on learning and knowing German, if you ask him to go back to not knowing German, can he do that? Impossible. German would have become a part of him. With this example, I intended to present that the Q is ridiculous, not the answer of anirvachaniyatva!
To extend the example further, if a person who doesn't know German and French was to be taught German through French, he would laugh it out as a joke. This leads us to a logic that one cannot learn another language without knowing one first. So not even going as back as how did the world bring languages, even to think only as back as how we learned our first language in this life, we face a seeming logical flaw that goes against the earlier logic that we established! These kind of things are inexplicable to logic, as we know, but still perfectly reasonable and justified.
The discussions on avidyA are meant to hone the intellect and understand the subject better; they are not to be taken beyond that since what the words can't describe can never be described. A person may take any of the above stands as long as it helps ones sAdhana to move ahead and not get stuck, since all are valid, invalid and somewhat valid from various angles of pAramArthika, vyavhArika and pratibhAsika satta. The thing to remember is that in either of the stands, one of the questions will still remain unanswerable and hence lead to anirvachaniyatva. A detailed analysis, of course is possible, with nyAya shAstra and things like that to refute/ support everything, but only to jog the brain and intellect, and thats that. :)