M-S technique does not produce an stereo signal by itself (it is not like X-Y or other "pure-stereo" techniques in which one mic points to le left and the other one to the right). You cannot just pan M mic to one side and S mic to the other.

To get a stereo signal (left-right) from the M-S (Mid-Side) you have to combine them through a special decoder matrix:
L=a*M+(1-a)*S
R=a*M-(1-a)*S

where a is a parameter between 0 and 1 that defines, electronically, the equivalent angle separation between left and right channels (a=0 is equivalent to 180 degrees between mics, and a=1 is equivalent to 0 degrees. Values between 0 and 1 are equivalent to angles between 180 and 0 degrees).

The reason lies on the behaviour of the bidirectional characteristic of the S microphone, as it generates inverse polarity if the same audio source is on the left or on the right of the capsule.

When you have not the decoder matrix, you can perform a similar function with your mixer. You can add M and S channel to get the Left signal, but you cannot subtract them, as the mixer only permits to add channels.

That is the reason why you duplicate S channel, shift its polarity and add it to the M channel. This is likely to subtract two signals with an "addition machine" like the mixer.

This a very special case in which you need polarity inversion (some times named, not rightly, as phase reverse). This has nothing to do with the problems of phase cancellation you can have with polarity errors in cables, different distances between two mics used with one source, or even with stereo techniques in which left and right capsules are not in the same place (distant or quasi-coincident techniques).

Apologize for the little maths.

Hope this can help.