I agree with that statement up to a point.Yes, to fail/flunk chemistry means you have failed the entire course and, if it is required for your diploma, you must take the course again. [...]
It seems to me that there remains a misunderstanding possibly due to a difference between British and American educational systems.That makes sense.
All I was pickily trying to make clear was that although flunking Chemistry could well mean you retake the test, the flunking and the possibility of retaking are logically separate.
You may flunk, then retake - and either flunk again or pass.
You may flunk, and decide not to retake - with various consequences.
You may flunk, and not be allowed to retake - with various consequences.
That just about covers it