Why does Mexican food taste dissonant with balsamic vinegar?
This is the same question, in essence as why any of these combinations are dissonant or unexpected:


Marina sauce on soba noodles
Cheese on Chinese stir fry
Haggis jambalaya


Every cuisine is a part of a culture, and there are cultural expectations for what is normal or not normal. 



A deeper question would be how and why such cultural expectations develop.

Note that this is a speculation, but an informed anthropological speculation:

Every cuisine is associated with a geographic region, where certain agricultural products are prominent.   The people in the area, quite naturally, learned to cook with the resources they had available.  So it would be odd for a mountainous culture like Tibetans to have seafood dishes, just as it would be odd for the inhabitants of modern day Shanghai to have Yakk milk dishes.

Over time, the culture adapts and finds flavor combinations and techniques that are applicable to its resources (stir frying in china, for minimal fuel use, for example).  These traditions form the backbone of the cuisine, and are how we recognize what is or is not part of that cuisine.



This allows us to make an educated guess as to why balsamic vingegar seems odd in Mexican food.

Mexico has not historically been a land of the grape, so they do not have a wine making or vinegar making tradition.  Therefore, a product like balsamic vinegar is not a part of their tradition.

Balsamic is also well identified with the part of Italy now called Modena, where it would have evolved because grapes were available, and there was a wine making industry already.

Putting the two together confounds cultural expectations.

Nonetheless, there are many chef's who enjoy and practice combining foods and technique across cultural and cuisine boundaries, and thus we have the modern practice of fusion cuisine.