Some really great thought breakdowns going on here! I'd like to try to tie everything together into one chunk, and knock out some lingering questions. Here's the simplified breakdown:
PREMISE
avoiding dairy --> eating fat less likely
avoiding fat --> avoiding heart disease more likely
CONCLUSION
avoiding dairy --> good health more likely
Notice a few things:
1) The statements involve comparisons, not absolute conditionals
These are not strict/absolute conditionals. It's not "if no dairy --> no fat". It's a comparative statement. If you avoid dairy, the that makes it
less likely you'll eat fat. Less likely than what?
Less likely than if you were eating dairy.
As a result, the idea that "eating dairy makes you more likely to eat fat" is completely supported. This is not an illegal negation, since the original statement gave us a comparison of "less likely".
If I said "Eating chocolate makes me happier" - what does that mean? Eating chocolate makes me happier than not eating chocolate does. So, eating chocolate makes me happier, and not eating chocolate makes me sadder. The original statement tells me both things.
2) The statements are applied in general, not as absolute rules
These are not strict/absolute conditionals. It's not "if no dairy --> no fat". The idea that 'avoiding dairy makes eating fat less likely' does not mean that every time you avoid dairy, you will ALWAYS be unlikely to eat fat. It means simply that, generally speaking, avoiding dairy makes eating fat less likely.
As a result, the conclusion cannot be taken down by a mere single instance of avoiding dairy not resulting in a higher probability of good health.
3) We can support the idea that eating dairy makes heart disease less likelyWe can combine the two premises. If avoiding dairy makes eating fat less likely, and avoiding fat makes getting heart disease less likely, then it seems reasonable to say that, in general: avoiding dairy makes heart disease less likely.
The problem, as a number of posters have pointed out, is that the conclusion makes the further leap to good health being more likely. Where did that come from!? Avoiding dairy might make heart disease less likely, but still make good health less likely in general - maybe a lack of milk gives you vicious toe fungus.
Darned if you do, darned if you don't. If you eat more dairy, you'll increase your chances of heart disease. But if you eat less dairy, you'll increase your risk of vicious toe fungus. Suddenly, the idea that avoiding dairy makes good health more likely is not so clear.
(A) Captures this possibility perfectly. The practice (eating dairy) may have potentially negative consequences (increased risk of heart disease), but the elimination (avoiding dairy) may also have negative consequences (increased risk of vicious toe fungus). And if that's true, the conclusion is no longer supportable.
Not the Problem
(B) This would be the flaw if the conclusion were "if you decrease your risk of heart disease, you must be avoiding dairy". The argument never claimed or assumed there was only a single way of decreasing risk.
(C) There's no recommendation language (ought, should, etc) anywhere in the stimulus.
(D) RelevanceThe evidence is surely relevant. It's not sufficient to guarantee the conclusion, but that doesn't mean it's wholly irrelevant.
If I said "I have plenty of pasta, therefore I have all the stuff I need to make lasagna", that evidence about the pasta isn't irrelevant! It's good to know! But it's not sufficient to support the conclusion that I have *everything* I need for making lasagna.
Now, if I said "I bought a pair of earrings today, therefore I have all the stuff i need to make lasagna", then you could accuse me of bringing irrelevant evidence to the table.
Information about increasing or decreasing the likelihood of heart disease is entirely relevant to the question of the likelihood of good health. It's just not the whole picture.
(E) All the statements, including the conclusion, are in probabilistic language - nothing shoots for a definite!
I hope this helps clear up a few things on this very sticky flaw question!