What political party did Teddy Roosevelt start?
The Bull Moose Party.
In 1912 the Republican party chose William Taft, the incumbent president as its choice to take on the Democrat challenger. In 1908, as the incumbent president, the Republican party chose Taft over Roosevelt which ruffled Roosevelt's feathers greatly.
To the 1908 Republicans, Roosevelt looked like a Progressive which in those days was synonymous with liberal. Roosevelt had been the driving force behind starting the National Parks System and was close friends with John Muir the naturalist. This did not sit well with old line Republicans.
But Roosevelt was still extremely popular among Republicans and he hoped that popularity would catapult him back to the oval office. All it did, as we have seen in recent past, was to divide the Republican party and help elect the relatively unknown Woodrow Wilson.
In a strange turn of events, Taft expressed relief at not being reelected. He went back to the judiciary, his first love, and some years later was placed on the Supreme Court and went on to become its Chief Justice. Historians seem to agree that Taft's post-president career far excelled that of his presidency.