This is a good question that deserves a serious answer. Without getting too complex, here is an explanation.
• The United States Congress has what is known as a single-member-district voting system. The winner of the elections in such systems is the one who gets the most votes, a plurality of votes. If the Blue Party gets 35 votes, the Purple Party gets 36, and the Red Party gets 29, the Purple Party gets the elected office. It’s a “winner-take-all” system; the other parties have no representation.
• Having elections set up this way tends to create an environment dominated by two parties, a regularity sometimes called “Duverger’s Law,” after the French political scientist who described it in the 1950s.
• Duverger contended that both candidates and voters cause this situation. Recognizing that a party can only win representation by coming out on top in a district election, politicians gravitate to the parties with a chance at victory. Voters also recognize that only the top two parties are really contenders, so they are reluctant to vote for parties that don’t stand a good chance of winning representation.
• In addition to the single-member-district elections, the United States has other electoral characteristics such as a presidential system and unlimited campaign spending that add to the dominance of the two parties. (In a presidential system, the head of government is also head of state, and the president leads an executive branch that is separate from the legislative branch.)
• The same factors that lead to two-party dominance in district elections are magnified in presidential campaigns and the two-party tendency becomes overwhelming. All but two of the states award their Electoral College votes in a winner-take-all fashion. (Each state receives Electoral College votes equal to that state’s representation in Congress. Maryland, for example, has eight congressional districts; each state sends two senators to the US Senate. Maryland, therefore, has 10 electoral votes that are cast in the presidential election.)
• It’s worth noting that third parties can influence elections. A third party can split votes off from one of the dominant parties, playing the role of “spoiler.” Voters casting ballots for such parties may contribute to victory of their least preferred party. And it’s true that a third party can also influence the agendas of the two dominant parties. They can provide a platform for important issues, even if the parties themselves don’t win the election.
In the United States, however, electoral victory by third parties is extremely rare at the local or state level. The last time a new 3rd party won the presidential election was in 1860 when President Abraham Lincoln won election as the Republican Party candidate. That victory was possible because the Democratic Party split in two over the issue of slavery.