You can see the logic underlying (A) in the stimulus’ analysis, but here’s another way of looking at it (incidentally, this argument form is called reductio ad absurdum):

Let’s assume having volitional powers does require thinking. Well, nonhuman animals have volitional powers, so that means they think! But nonhuman animals don’t think (because computers get closer to thinking than they do). So our initial assumption must not be correct – having volitional powers must not require thinking.

Here’s a translation of (B), taking the contrapositive to make it a bit easier to understand:

Everything with volitional powers is an animal.

The stimulus tells us some animals have volitional powers, but it doesn’t say animals are the only things with volitional powers.

In addition to lacking support in the stimulus, (C) fails a basic sanity check because “attributes” is a really broad category. Existence is an attribute. Being made of atoms is an attribute.

(D) says “all thinkers have volitional powers,” or “if you don’t have volitional powers, you can’t be a thinker.” That’s quite a strong claim – it’s a categorical rule.

The stimulus only gives us two individual examples: computers (which don’t think and don’t have volitional powers) and nonhuman animals (which don’t think and do have volitional powers). Two individual examples – regardless of what they say – can’t establish a general rule.

(E) is wrong because it makes a prediction about the future, which isn’t supported by the stimulus’ claims about the present. Time-based shifts like this are quite common on the test.