A little background: verb forms are different parts of speech based on verbs. For instance, the gerund
choosing, the participle
choosing used as a modifier, the verb
choose, the infinitive
to choose, are all different verb forms.
When SC answers offer you a choice among verb forms, the question tests either parallelism or idioms. (I haven't counted, but I think that choices among verb forms rarely turn out to require attention to
both parallelism and idioms.)
The question you refer to was--in it's original form--a question about parallelism. As another commenter, uh, commented the parallel marker
rather than means you need to make two logically comparable elements structurally similar.
OK, but what about your alternative sentence,
Many teachers choose seeking employment in the suburbs rather than facing low salaries in the city?
I don't think that that is idiomatic. My ear says that it's fine to choose to do something (choose to seek employment) or to choose a noun (choose a job search), but that it's not fine to choose a simple gerund (choose seeking).
A couple of important caveats: First, the GMAT is never wrong about the GMAT, including idioms. If you show me a right answer that includes
choose+simple gerund, I'm convinced. Second, verb-form idioms vary with forms of English, in a way that many other idioms do not. In particular, some uses of
-ing words (whether continuous verbs, participles, gerunds) that are perfectly natural in Indian English are awkward and unidiomatic in American English. Since GMAC has recently announced that they no longer test "US centric" idioms, I'd be surprised to see
choose+simple gerund tested. That's just my hunch about what "US centric" might mean, though. It's not GMAC's position, or even
Manhattan GMAT's guess.
Here's Stacey Koprince's excellent blog on the subject,
https://www.manhattangmat.com/blog/index.php/2011/09/21/update-on-the-gmat-changes-from-larry-rudner/.