This is a really interesting question. I'd love to get an explantion of how can I solve this CR question. Thanks in advance.

The conclusion: People who have suffered a serious stroke on the left side of the brain without suffering linguistic impairment must have their language centers in the right half.

Evidence: 1) The left (usually) or right half of the brain controls linguistic capabilities.
2) When a language center of the brain is damaged, for example by a stroke, linguistic capabilities are impaired in some way.

Assumption: Having a serious stroke will impair language centers. If this is NOT true, if a person can have a serious stroke without damage being done to language centers in the brain, then the conclusion is not justified. People with language centers on the left half could then have a serious stroke on the left side without suffering any language impairment. Again, the assumption is that strokes invariably damage language centers, as Choice D says.

Choice A need not be assumed. It might be that some parts, or all parts, are damaged and will never recover. This doesn't affect the argument.
Choice B doesn't have to be assumed. Other causes of linguistic impairment are irrelevant.
Choice C makes an irrelevant comparison.
Choice E might be true, might not be true . . . it doesn't matter.

I'm available if you'd like any follow up.

A. This statement holds no relevance to the conclusion made in the argument.
B. Here we are talking about the impairment caused by damage to language centers of the brain and we have derived a conclusion base on that only. Linguistic impairment caused by other reasons than damage to linguistic centers is not the concern.
C. We are not supposed to compare impairment caused by strokes or any other damage.
D. This is the assumption made in the argument. If we negate this statement and say that a serious stroke affecting the side of brain which consists the linguistic centre doesn't damage it then the whole conclusion would be wrong. So, it must be assumed that stroke would damage the part of brain. Hence, D is the answer.
E. The conclusion is about determining whether the linguistic centre is on left side or right side and not about whether only damages can determine the centre or not.