Some statisticians claim that the surest way to increase the

Understanding the argument -
Some statisticians claim that the surest way to increase the overall correctness of the total set of one’s beliefs is: never change that set, except by rejecting a belief when given adequate evidence against it. - Claim of statisticians.
However, if this were the only rule one followed, then whenever one were presented with any kind of evidence, one would have to either reject some of one’s beliefs or else leave one’s beliefs unchanged. - Hypothetical conditional. Premise.
But then, over time, one could only have fewer and fewer beliefs. - Fact
Since we need many beliefs in order to survive, the statisticians’ claim must be mistaken. - supporting premise + conclusion

Option Elimination - Flaw in the argument

(A) presumes, without providing any justification, that the surest way of increasing the overall correctness of the total set of one’s beliefs must not hinder one’s ability to survive - ok. Because statisticians, while making a claim, did not consider the "ability to survive." It may or may not affect the "ability to survive." Their concern is the "overall correctness" of one's beliefs. They talk about saying, "Fruits are good for health. And if any fruit causes you harm, remove that fruit from your diet to not fall sick." In the same analogy, the author claims that fewer fruits means fewer vitamins and minerals, and one needs more vitamins and minerals, so the claim of "if any fruit causes you harm, remove that fruit out of your diet not to fall sick" is wrong. No, that's not wrong; when we made that claim, we did not rule out the possibility that fewer types of fruits can lead to fewer minerals and vitamins. But we are just dealing with an aspect of the fruits that do not suit your health; we won't take them. Likewise, the author assumes that "statisticians' claims" should not hinder one's survival ability and concludes based on his assumption. The "statisticians" just never touched on that aspect. They are talking about the "correctness of beliefs," and the author is talking about the "number of beliefs" - two different aspects. The correct criticism from the author would have been that Mr. Statistician's "correctness" doesn't increase on what you suggested because of so and so. So, rather than directly challenging what statisticians said, the author talks about other topics, and citing that topic says you are wrong. This way of argument is flawed. This is so common in our business dealings. Through this argument, the test makers test our ability to deal with such complex real-life flaws.

(B) neglects the possibility that even while following the statisticians’ rule, one might also accept new beliefs when presented with some kinds of evidence - No. The statisticians claim clearly says, "Never change that set, except by rejecting a belief ." Adding a new belief is out of the question. So this is out of scope straight away. But yes, if we don't read well, and there can be a lot of reasons for that on exam day, then this is a great trap.

(C) overlooks the possibility that some large sets of beliefs are more correct overall than some small sets of beliefs - This is talking about, say, two sets of beliefs, or say, your belief and my belief. But that is not what this argument is concerned about. This argument is just concerned about one set of beliefs and the correctness of that. There is no aspect of comparison. This is out of scope.

(D) takes for granted that one should accept some beliefs related to survival even when given adequate evidence against them. No, oppose what the argument states.

(E) takes for granted that the beliefs we need in order to have many beliefs must all be correct beliefs - usage of familiar words to confuse the test taker. Distortion.