Perhaps the forbidden fruit was animal flesh, but I'd like to suggest another possible way this could be read.
In Eden, the first human couple was pure and not capable of desiring anything harmful (We might also consider that the devil tempted Jesus with bread, not flesh).
The sin was not anything they desired, but their lack of faith. In time, they would have gotten what they desired. They would have received more knowledge than they had 1 John 3:2.
In Eden they experienced nothing but good. But when someone first said God lied, Eve didn't just doubt, but believed strongly enough that God was pulling a fast one that she ate.
I'm not saying that this is the correct interpretation, just offering it as a possibility.