This question was quite confusing for me so I'm leaving my own explanation here.
From the passage, due to the fact that gold rings sell better than platinum rings despite having the same exact design, the author believes that consumers prefer gold to platinum. It does NOT say that customers prefer gold rings to gold platinum but is rather saying that customers prefer one material over the other.
This is a "weaken the argument" question; in this case, we want an answer choice that gives a different reason to why this trend exists, and more importantly a reason that deviates from the original theory that customers prefer 1 metal to the other.
Looking at the answer choices:
A) The passage and author's stance aren't about diamond, irrelevant.
B) Even if jewelers gave more importance to design, in this passage the designs are exactly the same, so this really has no impact, irrelevant.
C) This would give a reason as to why platinum was more popular than gold, but clearly in the passage this is not the case. So this answer choice is plain incorrect.
D) This and E could both be the correct answer. However, this is not necessarily as convincing as E because while platinum could take significantly longer to produce, it could also take insignificantly longer to produce; it's not clarified in the answer choice here. If it only takes a minute longer to produce than gold, that's not a very convincing case at all to explain the trend. Additionally, as bb said, if rings are produced faster than customers buy them, then this really isn't an issue, as inventory size wouldn't be an issue for customers, making this point moot.
E) This seems to be the "more correct" answer, because not only does this say that gold is cheaper than platinum, but that it's CONSIDERABLY cheaper than platinum. This means that there is a very noticeable difference in price, as compared to choice D in which we don't know the severity of production time. As a result, this answer choice provides a much more convincing alternative reason as to why customers prefer the gold rings over the platinum ones.
E is correct.