You can't restrict it like that. If you cut your finger by accident and pierce the skin, you may also say "Ich habe mir in das Fleisch geschnitten." This does not mean you are going to eat your finger. In my opinion "the flesh" should be a valid translation as both flesh and meat translate to Fleisch.
Its the context. So we are learning about food correct? Well 9 times out of 10 you will never hear anyone say "mmmmh that peice of flesh looks good" so given that we are learning about food and not say anatomy then it makes sense that the translation would be wrong. In languages context is a huuuugr factor.
They're talking about English.
das Fleisch - the meat, the flesh
Flesh and Fleisch are related words, though, along with Dutch vlees and even Swedish fläsk.
Most people using this are trying to learn how to speak and read German, not just translate it to English. Since the gender of nouns is so important, they're typically shown with the definite article to identify the gender. If it just said "Fleisch". you'd be lost on the gender. But you still have to be able to identify the definite article for what it is. A good practice using this tool is to stop trying to think in English grammar for all the answers.
Just looking at the phrase for one second implied to me that the word could also mean flesh- but I was going to ask is there a more sensual term for the word flesh, after all- you wouldn't want to say someone has nice meat- even if you do want to comment on how nice their flesh is. (Kind of a creepy question sorry, but I am interested in knowing if there is)
Is it another one of those situations where the word can mean entirely different things after you consider context, articles, case, and changes to suffix?
In an entirely non-food sense, the flesh would be my first response- but it's easy to interpret it as the meat given we're talking about food.
"Pleasures of the flesh" "I'm eating cow flesh"
Both sound kind of wrong, but for completely different reasons. I hope this isn't considered inappropriate as it's just speculation and curiosity.
Sometimes looking at the ending of a word helps. Anything ending in "-ung" is female, for example. I've seen extensive lists on that one, but I think trying to remember that is more trouble than it's worth. In everyday encounters, no one will mind if you use the wrong gender for a word.
All you people talking about context are kinda dumb. A word is a word, and "the flesh" should be accepted because fleisch also means flesh. It might mean meat in this context, but it wouldn't in others, and so either interpretation is acceptable. Don't punish people for making linguistical connections between languages.