How did Aaron Burr first anger Alexander Hamilton ?
Long before their duel in July of 1804, which left Hamilton with wounds that would kill him, Hamilton and Burr had been rivals. Their initial disagreement arose from a 1791 U.S. Senate race in which Burr defeated Philip Schuyler, who was Hamilton's father-in-law. Hamilton, then Secretary of the Treasury, was relying on his father-in-law's support for his fiscal program, which was in support of Federalist policies. Burr, on the other hand, was an anti-Federalist (later a Democratic-Republican, called Republicans for short).
In 1800, Burr published a tract Hamilton had written to privately criticize John Adams, then the President. Burr's publication of this document embarrassed the Federalist party. The rift between Burr and Hamilton widened with the election of 1800, in which Burr and Thomas Jefferson deadlocked. Hamilton threw his support behind Jefferson in the House of Representatives (which had to decide the election), who wound up becoming President. Burr became the Vice President under Jefferson. Finally, in the election of 1804 for Governor of New York, Hamilton again opposed Burr's campaign, and Burr wound up losing the election. The event that precipitated their duel was a remark that Hamilton made at a social event about Burr; the remark, made in 1804, had to do with Burr's personal character.
Burr and Hamilton met in a duel in Weehawken, New Jersey, on July 11, 1804. They had dueled with other people before. Each fired shots from their pistols; Burr was not harmed, but Hamilton was hit and died the day afterward. Burr, who was indicted but later acquitted on charges of murder, was hoping to revive his political career with the duel; however, the duel effectively ended his career.