They say a week in politics is a long time. Like politics, a week is a long time in teaching too!
This option is eliminated because of wrong comparison. Also, "as politics, a week" is certainly wrong. Eliminated
Your analysis is very good. However, the reason for eliminating Choice B - "As" - is not correct. When "As" is used for comparison, it MUST be followed by a clause. In this option, "As" is just followed by a anoun. "As" can ONLY be followed by anoun, when it presents role or function of someone/something. For example:
As a manager, John has made significant contributions in the company.
Here there is no comparison between "John" and "manager". Rtahre "john"himself is the "manager". His role in the company is of a manager.
Since Choice B in the given problem "As" is not followed by a clause, it now illogically presents the function of "a week" as "politics".
To learn the correct usages of "Like" and "As", click on the following link for a detailed article:as-vs-like-correct-and-incorrect-usages-133950.html
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Hope this helps.
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