Though vs While

Solution 1:

SAT rules require test takers in the Verbal sections to weigh the answers and compare two good answers. Two plus two is four, but in language, there are shades of meaning that the College Board tests. One answer may be suitable, while another is superior.

In your sentence, while serves the sentence but though does a better job. While means that at the moment of your judgements, your opinions were not identical as to the cause. Though emphasizes that your opinions oppose each other, which they do. That reasoning makes it the answer the test seeks. The American Heritage Dictionary of the English Language, fifth edition, offers the following information:

Usage note for while:

As a conjunction, while is used to indicate that two events are happening at the same time … .

A definition for though:

  1. Despite the fact that; although.