Because if it were to be on the left side the wing on the front crest would either cover it or put the C in a awkward position on the jersey. They changed it when the jersey changed from CCM to Reebok.
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I stand to be corrected, but I think it has to do with the redesign of the new uniforms a couple of years ago. Because of the placement of the logos, the C and A had to placed on the "wrong" shoulder.
The logo on the New Jersey comes up to where the 'C' would be on the left side, so they moved to the right side.
Detroit did this last year because they had an extra patch on the left side already so they put it on right. I guess they stuck with it this year.