Q:

"Süß und sauer" vs "Süß und herzhaft"

I've been watching the series "Jojo sucht das Glück" on DW.   In it, the main character Jojo talks about how Brazilians would make "süß und sauer Speisen", but the German family doesn't understand the phrase.   Instead, another character suggests "herzhaft" (savory) instead of "sauer".   Does German not have "sweet and sour"?   
Link to episode 12.   Discussion on Sweet vs Sour starts at 1:40. 
https://www.youtube.com/watch?v=sQ1uuAFA8y0

A:

Generally, if you want to discern sweet food from unsweet food, I would say your suggested "süß" vs. "herzhaft" is the most practical way. 
One thing that could be interesting in this context is that there is a category of "süß-sauer" foods.  That's predominantly food coming from Asia (or being sold to us as such).  This usually refers to some sauce poured over it that has both in abundance, sugar and some sour ingredients such as vinegar or lemon.   

A:

There is not really a good single word opposing "sweet" in the context of food. " Sour" is the traditional antomym ("sweet and sour" is a phrase with strong collocation, "sweet and salty" less so), but it does not quite get to the point for dishes.  This is because we actually construct food mostly in categories of "sweet" and "non-sweet", but concrete dishes can fall into any combination of "sweet", "salty", and "sour". 
This "problem" is a fact that native speakers are aware of.  So if one wants to describe the "non-sweet" category of food, one can choose among some words which cover most of the category, and by context, hope that it will be known what is meant.  
For me, as an Austrian speaker, I would preferentially use pikant or salzig, mostly.  Herzhaft I do not use in spoken language, but understand as being at the same level as pikant.  I also think that I often just say nicht süß, or (a bit playfully) unsüß, because I am aware of the problematics: potatoes and bread are neither salty, nor pikant, but definitely constructed as "non-sweet".  
I think I do not really use sour.  But as an anecdote, I once was in a specialized gastronomy store, where next to the "sweet dumplings" section there was one titled "sour dumplings".  Out of interest, I went to look what "sour dumplings" are, just to find out that they actually meant "non-sweet dumplings", such as Semmelknödel or Kartoffelknödel, which are in no way "sour".  So apparently, "sour" is used in this way as a technical term, but it might surprise people not in the know. 