Lets first understand the difference in the meaning of "as" and "like".

X as Y => X actually functions as Y
X like Y => X behaves like Y

For example:

Tom works as a football coach. = This implies that Tom is actually a football coach.
Tom works like a football coach. = If this sentence is correct, then it implies that Tom is not really a football coach, but he behaves like one. May be he is as disciplined as a football coach is or he devices strategies in his workplace as a football coach does.

Sam acts as Susan's mentor. = This implies that Sam is actually Susan's mentor.
Sam acts like Susan's mentor. = This implies that Sam is not Susan's mentor, but he behaves like one.

In the light of the above meaning difference, now lets analyze the sentences that you quoted from OG.

A) I work as a librarian.
B) I work like a librarian.

Clearly, the more obvious meaning is that I actually work as a librarian. This meaning is expressed by (A). Now if the meaning is "I am a librarian", then clearly (B) does not express that meaning and hence is correct.

C) It felt as a dream.
D) It felt like a dream.

Clearly, the author is comparing an experience to a dream. Thus, he does not really intend to say that that experience (it) was actually a dream. This is expressed by (D).

For e-GMAT customers, the difference between as and like and many other commonly confused word pairs is covered in detail in two concept files "Idioms - Functions I" and "Idioms - Functions -II" at e-GMAT.

Thanks,

Payal