The literary antecedents for much of James Baldwin's work are Richard Wright's books, the most famous of which is Native Son. This is true, though Baldwin and Wright had personal disagreements, and Baldwin was critical of Wright's portrayal of the African American experience. To understand why Baldwin regarded himself a "native son," however, we should look at the implications of Wright's use of the term as the title of his 1940 novel.
In Wright's Native Son the central character, Bigger Thomas, is a young man Wright depicts as emblematic of much of the African American experience. To be a "native son" is to be not only typical of those born in one's country, but to be, in some sense, a result or product of that country's inherent features. In the case of African Americans, that result, as Wright sees it, is the alienation of living in a society in which race is a defining factor and is used by the white power structure to oppress black people. Bigger's thoughts and behavior, and ultimately his tragedy, are conditioned by this unfair and oppressive system.
James Baldwin regarded Wright's portrayal of Bigger as, to some extent, a negative stereotype, despite the fact that Wright himself was African American. But Baldwin nevertheless identified with Bigger Thomas's sense of victimization in the America of the pre-Civil-Rights era. Whatever his personal and literary disagreements with Wright, Baldwin accepted the term "native son" as a correct description of himself in his own struggle to express himself and to break free of the restrictions of an oppressive society.