Why did the two party system developed in the US?

A quick answer is that the indirect method used to elect the president makes it highly desirable for one candidate to win a majority- more than half of the electoral votes. This means that only two very strong parties have any chance of winning the election. A third party party can only be effective as a spoiler.

Therefore what happens is that one party wins and is "in". The other party tries to unite everybody who is unhappy with the in government or life in general . If you do not like the present, you join the opposite party and hope for the best. This makes for a lot of compromise .

The framers of the US Constitution did not envision the emergence of political parties and they surely did not set up a two-party system, but parties formed in time for the third election. At that time, there were two major visions of the federal government and two influential men to lead advance each vision, so two parties formed naturally. There was somewhat of a geographical division as well, one party stronger in the North and the other in the South. In 1824, the situation was more complex with Western settlers and recent immigrants beginning to take an active role in politics and in that year, four mostly regional candidates roughly split the vote, sending the election into the House to decide. Andrew Jackson led in both popular vote and electoral vote was not made President by the House. Consequently, Jackson supporters began to build a national party that could win the an outright majority in the House and they succeeded . The opposition to Jackson saw that they needed to band together and form a new national party if they even wanted to defeat the Jackson Democrats. Thus the Whig party was formed. The these two parties controlled the White House until slavery became an overwhelming issue and the parties both split and a new anti-slavery, mostly Northern party, the Republican party was born. After the slavery issue was settled by the Civil War and Southern states were allowed to vote again, a new party was formed , essentially to oppose Republican rule which had become corrupt as well as being no friend of the defeated South. Since then, each of these two parties has developed a base philosophy ,which changes slowly and each year each party tried to attract enough people outside their base to win.