The first premise establishes that the desire for praise is the desire to obtain the favorable opinions of others. (A) would establish that helping others mainly out of the desire for praise constitutes an action that is NOT motivated by a desire to help others. This then would connect with the second premise, which takes us to “not deserve praise.”

The conclusion concerns people who help others “primarily” out of a desire for praise. (B), which tells us that actions motivated “solely” by praise don’t deserve praise, doesn’t cover actions that are done “primarily” out of desire for praise.

We don’t know that people who help others primarily out of a desire for praise are indifferent to the welfare of others. Maybe they do care about others...it’s just that their action is mainly about getting praise.

It’s not clear that one who helps others out of a desire for praise is actually advancing their own interests. It’s also not clear that helping others out of a desire for praise wouldn’t advance the interests of others. So (D) doesn’t connect to any of the premises of this argument.

(E) establishes that motives determine whether one deserve praise. But (E) allows for actions out of selfish motives, such as desire for praise, to still deserve praise. (E) doesn’t tell us what kind of motive would make an action undeserving of praise.