[pacaro]

Granted, the intersection of precedence and associativity is a great source of confusion (and any number of annoying Facebook memes)

I'm not a formally trained mathematician, but one way to rationalize + and - having the same precedence, is to consider them as inverses of each other, so your two examples can be written as

a + -b + c

And

a + b + -c

At which point precedence and associativity no longer matter. The same can be done with multiplication and division