If both sides are weak, respond tightly, pressing any advantage you have.
If the opponent is strong, balance local points and strength with side development and centre access.

The symmetry is more an indication of patterns of best moves rather than anything general. If the opponent doesn't play joseki, you shouldn't mirror. However, the question remains as to why josekis have mirrored outcomes.

A partial answer is:
1) if the opponent has a good move at A, the mirror option is obviously a good move too. (though it might not work with the previous move)
2) the opponents best move is your own

Hence, play the mirror.

This implies the joseki assumption
3) Moves are focused on the corner, assuming empty space (all else equal) on the sides.

The normal deviations from the mirror are due to strength and weakness
a) If the opponent plays too close, you may play closer to them to attack
b) If you have extra support (e.g. first move in the corner), then you can try to claim slightly more with your 2nd move (normally that means play 4th line rather than 3rd).

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Actually even the importance of "miai", dividing by 2 arises because there are 2 players, so in order to guarantee a defence you need 2 available options. This can be generalised to more complicated fighting situations. An approach move to a shimari might not have a direct threat on the corner (the shimari can normally defend in sente), but the aji makes it difficult to pincer when the approach stone also has 2 options of running out and the corner. This balance topic doesn't seem to be talked about much.

In the same vein, the shimari pretty much just needs one more move to defend the corner solidly even against an approach, which is why it is so valuable to approach. You make miai of corner aji and the side.