At the time Hamilton wrote the Reynolds Pamphlet, it was starting to look like the story of his affair with Maria Reynolds was about to become public. In the summer of 1797, a man named James Thomson Callendar began writing a series of pamphlets targeting Hamilton and threatening to expose scandals from his time as Secretary of the Treasury. The alleged charges that he made against Hamilton cited documents from James Reynolds, which Callendar claimed were evidence of illegal speculation - an alleged attempt by Hamilton to enrich himself while serving in government office - rather than evidence of an affair. Hamilton hoped to set the record straight.

As shown in the musical, some Democratic Republicans were aware of Hamilton's relationship with Maria Reynolds, but had sworn themselves to secrecy on the matter. By the summer of 1797, it looked like one of them had let the secret slip (possibly James Monroe), so Hamilton tried to get ahead of the story by disclosing the whole story in great detail. Here's Ron Chernow's account of Hamilton's attitude while writing the Reynolds Pamphlet:

"Hamilton now reverted to lifelong practice: he would drown his accusers with words. In mid-July, he holed up in a Philadelphia boardinghouse with his friend Congressman William Loughton Smith of South Carolina among the tenants. As he confessed his sins, Hamilton probably did not want to face his family. One pictures him stooped over his desk, scratching away at a furious pace. According to Smith, Hamilton wrote with zest and a vengeful glee. He 'was in excellent health and in very excellent spirits, considering his complicated situation.' Months earlier, Hamilton had complained to Smith of feeble health. Now, he burst forth in fighting trim, striking a note of bravado as he confronted his enemies." [Hamilton, p. 533]

Hamilton wrote 95 pages - 37 pages of personal confession plus 58 pages of supporting documentation - describing the exact details of the affair, the Reynold's blackmail, and Hamilton's payments of hush money. Basically, Hamilton thought that by coming clean about the affair, he could control the narrative and definitively clear himself of the accusations of corrupt financial dealings. He was wrong, and his political career suffered as a result.