Hey All,
I didn't check the other thread, but I thought I'd add a few more details in here. As some have said, it is a comparison issue, but the notion of comparing "actions" versus "things" is a dangerous one. I warn you that the explanations below are complicated, so feel free to ask follow-up questions. First, let's consider a simple comparison example:
Like running, swimming is great.
No one would argue that we aren't comparing actions in that sentence, but these are gerunds (verbal nouns), so we have to use "like". Thus the distinction between "actions" and "nouns" starts to break down. Now watch this:
Like Einstein, Dave was a really smart guy.
You could argue here that we're comparing people (Einstein and Dave) OR actions (they were both smart guys), yet we still need "like".
In reality, we only use AS when comparing CLAUSES (a phrase with a verb in a tense). "Like Einstein" has no verb in a tense, so we use LIKE. Similarly, "Like running" doesn't have a verb in a tense, so we use LIKE. Let's consider the answer choices in this light...
257. During an ice age, the buildup of ice at the poles and the drop in water levels near the equator speed up the Earth’s rotation, like a spinning figure skater whose speed increases when her arms are drawn in.
(A) like a spinning figure skater whose speed increases when her arms are drawn in
PROBLEM: Believe it or not, in this iteration of the sentence, LIKE is more correct. Think of it like this. I could correctly write, "Faster and faster turned the merry-go-round, like a spinning figure skater." In this sentence, the second phrase has NO VERB in a tense, so LIKE is okay (we're comparing the NOUN "merry-go-round" with the NOUN "spinning figure skater" (spinning is an adjective there)).
Now before you all get up in arms, obviously this answer choice is in correct. We WANT to compare actions (namely the way that the Earth's rotation speeds up, as well as the skater's rotation). But in this answer choice, if we just threw in AS, we wouldn't have the verb that we need to make this a clause. The verb "increases" is inside a modifying phrase, initiated by the relative pronoun "whose", so we lack an actual action to be comparing. Complicated, I know, but a critical piece of information you must understand to answer these brutal comparison/modifier questions. (I'd also add that the wording of this particular sentence makes it sound like we're comparing "rotation" to "spinning figure skater", which makes it even more wrong.)
(B) like the increased speed of a figure skater when her arms are drawn in
PROBLEM: Comparison logic. It's not the increased speed we want to compare to, though the LIKE is correct (this isn't a clause, as the verb "are drawn in" is within another modifying phrase, initiated by the relative pronoun "when").
(C) like a figure skater who increases speed while spinning with her arms drawn in
PROBLEM: Comparison logic. It's not like a figure skater who increases speed with her arms drawn in, but it's like THE WAY speed increases when the arms are drawn in (as nitya said, we need the clause, not the noun).
(D) just as a spinning figure skater who increases speed by drawing in her arms
PROBLEM: Fragmentary. Just like we saw in A, the "who" phrase is a modifier, so we never get a main verb here, meaning we CANNOT use AS correctly here. It would need to be something like "just as a spinning figure skater who draws in her arms increases her speed". Now we have the verb "increases" as a main verb, so we're allowed to use "as".
(E) just as a spinning figure skater increases speed by drawing in her arms
ANSWER: Voila. We get the AS, and the main verb "INCREASES".
As I said above, I'm happy to answer follow-up questions here. Hope this helped!
-t