In some versions of our diagram, it looks like a decent amount of correctly addressed mail ends up damaged (the ✓ marks in the 3+ day group). But that proportion is variable. Since the stimulus says nearly all correctly addressed mail arrives within 2 days, the damaged portion could be tiny:

Here, only 1 out of 10 correctly addressed pieces is damaged. That doesn't seem like a "large proportion." But even if you think it's still large, we could make the ratio even more extreme. Just imagine only 1 out of 1 million correctly addressed pieces is damaged.

In our stimulus visual, we placed ✗ marks in the 3+ day group because that's what we needed to make 3+ days the majority. But nothing in the stimulus says incorrectly addressed mail can't arrive within 2 days. We could just as easily draw some ✗ marks in the 2-day group:

So we can't conclude that no ✗ marks land in the 2-day group.

(C) is trying to reverse the relationship in the first sentence. That's the cleanest way to understand why it's wrong. "Nearly all A are B" does not prove "Most B are A." Unfortunately, if that's not enough to convince you that (C) doesn't have to be true, we do have to get into some example numbers.

The stimulus tells us that of all correctly addressed mail, nearly all arrives within 2 days. But knowing that nearly all ✓ marks land in the 2-day group doesn't mean ✓ marks dominate that group. There could be plenty of ✗ marks in the 2-day group too:

In this example, nearly all correctly addressed mail (4 out of 5 ✓) is in the 2-day group. But the 2-day group has 9 pieces total, and 5 of them are ✗. Most of the 2-day arrivals are actually incorrectly addressed. (C) doesn't have to be true because a large volume of incorrectly addressed mail can flood the 2-day group, as long as we add enough 3+ day mail to offset the additional number added to the 2-day group.

See the stimulus analysis to understand why (D) must be true. In order for most (over half) mail to arrive in 3+ days despite almost all correctly addressed mail arriving within 2 days, there has to be a large proportion of incorrectly addressed mail in the total pool. Otherwise, we wouldn't have enough 3+ day mail to say that over half of mail arrives in 3+ days. And as we saw, the stronger the phrase "nearly all" is (the closer it gets to "all"), the larger the proportion of incorrectly addressed mail has to be. No matter the example numbers we use, a large proportion of the total mail must be incorrectly addressed.

Most mail arrives three business days or more after being sent. But (E) is comparing two different groups: mail arriving within 2 days and mail arriving between 2 and 3 days. We don't have any information restricting how much mail falls in the 2-to-3-day window. A large amount of incorrectly addressed mail could arrive between 2 and 3 business days, making that group bigger than the within-2-days group.