Hi Swati,
Ok - so we're trying to find an assumption that the author relies on. I.e, if the assumption isn't true, the argument doesn't work.
With that in mind, let's take a look at option D:
"The difference in the interest rates paid to depositors by different banks is not a significant factor in bank failures."
There is nothing in the argument, implicit or explicit, that has anything to do with interest rates. The author says that insurance is "partly" responsible, thus acknowledging that there may be other factors.
If (D) is the answer, the argument should not work without this assumption. But even if we say that interest rates are a significant factor, the argument is not affected to a high degree.
You are correct in that (D) would be a good answer in the following two cases:
1) The author stated that insurance was the only significant factor / only factor / the sole reason / etc...
2) The option (D) stated that "The difference in the interest rates... is not the sole factor in bank failures.
Be careful in distinguishing assertions that take on an extreme viewpoint vs a flexible viewpoint.
Hope that clarifies.