The view that every person is concerned exclusively with her or his own self-interest implies that government by consent is impossible.
Conclusion
Social theorists who believe that, "People are concerned only with their self-interest" evidently believe that, "Aspiring to democracy is futile".
translation: if you think "People only care about themselves", then you believe "we're not gonna get democracy"
Evidence
You can't get democracy, unless you have a government by consent. And, the view that "People only care about themselves" imply that you can't get a government by consent.
Evaluation
Okay, this was terrible. The most important thing to notice would be that what we're trying to prove in the conclusion is a conditional statement about someone's beliefs.
Valid inference: Mark is a 3-time pig racing champion. Samika had dinner with Mark. So Samika had dinner with a 3-time pig racing champion.
Invalid inference: Mark is a 3-time pig racing champion. Samika knows she had dinner with Mark. So Samika knows she had dinner with a 3-time pig racing champion.
Why is the 2nd one invalid? Because we don't know if Samika actually knows that Mark is a 3-time pig racing champion. We know it, but she might not. (He might not bring it up on a first date)
Similarly, we know, from having read these premises, that if you believe "People only care about themselves", then you have logically committed yourself to the idea that government by consent is impossible, which would make democracy impossible.
But you might not realize those implications/consequences of your "people only care about themselves" belief.
So it's not right to say that if you believe the first thing, you also believe that "democracy is impossible'. You might not realize that the latter is an inference that can be derived from the former.
Goal
Look for an answer explaining that the author is presenting a logical chain of beliefs, and then illicitly assuming that someone else is aware of this logic chain of beliefs.