In Frankenstein, why does the monster see himself as another Adam?
The creature sees himself as another Adam because, as he says, he was "created apparently united by no link to any other being in existence [...]." The creature recognizes that he was made in a unique way, as a unique being who has nothing in common with other men. Further, his creator made him alone, without a mate, as Adam was created prior to Eve. Now, the creature feels entitled to an Eve of his own, and so he's returned to ask his creator for such a mate.
However, just as the creature feels that he should be Victor's Adam, beloved and cared for, he feels that he is actually more like Satan because "like him, when [he] viewed the bliss of [his] protectors, the bitter gall of envy rose within [him]." God created Adam to be his perfect creature, and God loved him; however, Victor created a monster, and then he proceeded to neglect and spurn him. Therefore, this monster becomes jealous of the DeLaceys because they are beautiful and happy, as he feels he ought to be, as he feels he has a right to be as Victor's Adam.
Soon after the monster learned how to read, he came across three books in a box. One of the books talked about the creation of Adam and how God was at war with the other heavenly creatures. The story of Adam’s creation made the monster question the whereabouts of his creator and wonder if his creator abandoned him like God cast down Satan. The monster, based on what he had read, believed that just as God created Adam, so had Frankenstein created him; in that sense he was similar to Adam. In addition, the monster had no companion and was lonely—just like Adam was before the creation of Eve. The monster tried to convince Frankenstein to create a companion for him to assuage his loneliness and sadness.