why does Hester feel she must reveal the secret?

Reveal? It isn't until the end of the novel that Hester, Pearl, and Dimmesdale decide to leave for Europe in the hopes that they can live as a family without shame. Just before, Hester learns that her husband is planning on exposing the minister as Pearl's father, so Hester mounts the scaffold once again with her daughter, without the scarlet letter, and wearing her hair down like a maiden. Dimmesdale joins them there, and then he dies.