"ah, the romantic soul! ” said my parents skeptically, worried that my business would fail, that i was behind the times.
based on this stanza, how do the speaker’s parents feel about her decision to pursue book publishing?

Based on these lines, it seems like the parents wish that the speaker had a more reliable profession. The fact that the parents are skeptical indicates that they most likely do not think that book publishing is a profitable pursuit. Moreover, they seemed worried about the fact that book publishing is disappearing, so they believe that the author might be behind the times.

credit should be the answer