Ah, one of the great myths of the French Revolution.

Did Marie Antoinette ever say this phrase? If she did, no contemporary accounts of it exist. It wasn’t until later that the quote began to appear, though it did appear in multiple sources. This isn’t a case of one person inventing the story, and then everyone else cites that one book. But, still, there’s certainly reasonable doubt that it ever happened.

The next question is asking what the quote actually was. The original quote is: “Qu’ils mangent de la brioche.” This is translated to ‘cake’ because brioche wasn’t a staple food in the English speaking world. Now, of course, most people know that brioche is a bread with an enriched dough, not a cake. Bread itself was very expensive, constituting a significant portion of common man’s pay. Much like Bill Gates not being able to tell how much things from a supermarket cost, the idea most people take from this quote, and the idea attributed to it in original writers such as Jean-Jacques Rousseau, is that she had such little idea of what the peasantry’s life was actually like that she believed that if they were out of bread, they should just eat brioche, not understanding that if they were out of bread, they certainly never had the means to acquire brioche to begin with.

So, yes, I would say your teacher was likely full of malarkey. “Brioche” is decidedly not a waste product of baking bread. The actual veracity of the quote is questionable, and even if the quote was said, it was never discussing cake.