The two-party rivalry isn't new they seem to be natural rivals, in this article I hope that I can summarize the two parties' history and goals please note that not every aspect of the parties is mentioned but is summarized to fit in this article.
The Republican Party is also known as the Grand Old Party (GOP), originating from the opponents of the Kansas and Nebraska act of 1854 which helped spread slavery to the north of America, keep note that at this point in time the United States of America (USA) was divided into two the northern non slavery driven economy and the southern slavery driven economy. The party's first President was Abraham Lincon under Lincon's leadership slavery was banned in the USA. The Party significantly shifted from its origin now mostly supported in southern states more specifically in rural areas.
The Democratic Party can be tracked down to supporters of Andrew Jackson the seventeenth president of the USA, the Democrats were also part of the Confederates during the American Civil war. They were mostly supported in the southern states until the Roosevelt reforms at the beginning of the 20th century which shifted the Party into a more liberal stats, thus the south the more conservative part of the party split to join the Republican Party
The two parties have very different political agendas one more conservative than the other, they used to work in harmony but in recent reports, both sides seem to have become more and more radical to each other. This is a very dangerous trend, it is very important to
un-radicalize and work in harmony.