Why Mirror Image Position

I don't know but I could make an educated guess. I suppose it's because some piece configurations are advantageous compared to others and thus unmirrored position could potentialy hand one of the players much bigger advantage than the normal first move advantage white has. After you play some chess 960 you notice that you occasionaly get really akward starting positions where every piece appears to stand badly but at least you can console yourself with the fact that opponents pieces stand just as akwardly.

I thought it was pretty obvious really, that some piece configurations are simply better than others (easier development, better centre control, fewer weak squares, etc); and as such it's only fair to give both sides the same configuration. Or in some cases there might be one configuration that is especially effective against another specific one, e.g. if it's easy to develop pieces in the former to attack weak points in the latter. Though this doesn't solve the issue of there potentially being configurations that give a significant advantage to the side that moves first (or maybe even the one that moves second!) when played from a symmetrical starting position (okay, admittedly this does exist in the standard configuration, but only on a small scale); but hey, that's what the reversed-colour rematch is for.

That's some pretty fuzzy logic there. The starting configuration in standard chess is symmetrical too, yuh? (Unless you're implying that standard chess counts as "very drawish" too, which is admittedly a slightly plausible claim given the percentage of drawn GM games; but I wouldn't really say that counts as very drawish. In any case, IMO it's not a good idea to solve a drawish situation by flipping a coin to decide which side gets a dagger and which side gets a machine gun. (which, in case you didn't get the analogy, is meant to represent what might happen if the two sides had randomized but different starting configurations. (I really need to stop explaining my jokes. (wow, how many brackets have I nested in this sentence now?))))

P.S. regarding copying moves? That's a strategy that specialists in the field would describe as, to use a technical term, "very bad". Well, anything past the first few moves at least.

The advantages of certain piece configurations over others might be largely irrelevant in beginners games but when the players skill increases smaller and smaller details become important. Certainly I think in chess 960 one of the players can enjoy much larger advantage than the advantage of having white pieces in regular chess. The colour advantage in regular chess is already pretty significant as one can witness by looking at statistics from large databases. So, why to increase this advantage unnecessarily.

I think your logic: if one piece stands badly then some other piece stand better is incorrect. Different pieces have got different properties and thus also different squares are good for different pieces. Now, it might be just because I'm accustomed to normal chess but I feel that the regular starting position is actually pretty close to ideal. For example in regular chess the moves e4 and d4 are often very good because they both open the way for bishops and combat the centre. Switch the starting places of the rooks and bishops, however, and the only way to develop the bishops is to move the b/g pawns but these pawn pushes don't combat the centre. I seriously suspect that people who invented the rules of modern chess planned things so that the starting situation allows for fast and easy development so that fighting contact is established soon.

A better example of squares good for one piece but bad for another IMO: bishops vs knights on corner squares. Having your bishops on corner squares is pretty okay given that it allows, as you mentioned, a one-move fianchetto; but having your knights on corner squares is pretty awkward.

Also, as I pointed out in my earlier post, I don't agree with the argument that "it's fair because it's random". IMO chess should be entirely a game of skill, with no luck involved; so it's not fair to flip a coin to decide which side gets an advantage. (Again, as I mentioned, admittedly the first-move advantage is an example of this; but I think it's less significant than what could happen with an assymetrical setup.)

There is a variant called "Double Chess 960" which is the same except it is not mirrored.  However, since some piece configurations are better than others, this wouldn't necessarily be a fair game.