Why has the two party system dominated US politics?

Because you have a stupid voting system in which any plurality can govern.

Where I live it takes a majority-coalition. As  a result we now have 17 parties in the "second chamber"

Because the two parties have vastly different ideas for the country.  The Republican party didn't exist until about 1856 and was formed with the primary goal of ending slavery.  The Democrat party fought a war to keep slavery.  Now we have Democrats ending our republic or at least having those designs in the plans they have revealed.  The Republicans are trying to preserve our republic.  The parties are polarized to the extent that there can be very little compromise between them.  Its been worsening year after year.

Because it is consistent with the human body. Left and right, two eyes, two ears, two legs etc. 

Because people refuse to get out of the mold. They believe if you vote third party, it is giving your vote to another party (which as of now, is true). But, we did have one president that was of no party - George Washington. We did have the Democratic-Republican party. We did have the Whig party. 

Because we have a winner-takes-all system that requires people to get a majority of votes and don't have things like ranked-choice voting.