The basic reason why the Bull Moose Party was formed is that Theodore Roosevelt wanted to get elected president in 1912. He was upset with the way that the Republican Party had gone after he left office in 1908 and he wanted to run against President Taft.
Roosevelt was the first of the progressive presidents. When he was planning to leave office in 1908, he picked William Taft as his successor. He believed that Taft would continue his progressive policies. However, Taft's presidency did not go the way TR wanted it to. Although Taft did many progressive things, he did not satisfy TR. Among other things, he fired one of TR's proteges, Gifford Pinchot, a staunch conservationist. Most historians argue that Taft really was no less of a progressive and they say that TR's main motive for opposing Taft was ego.
So, the Bull Moose Party formed because TR disliked what Taft had done and he wanted to be president again.