The most common answer to this is that Theodore Roosevelt picked William Taft because he believed that Taft would essentially follow what he, Roosevelt, had started. Roosevelt expected that putting Taft in office would, essentially, lead to the same policies as if Roosevelt himself were still in office.
Taft was a popular figure and was therefore likely to win election. He had held many high positions and was respected for his intelligence and his dedication. Roosevelt felt that Taft would be easy to elect and would be fully competent to carry out Roosevelt's policies. In a sense, Roosevelt felt he was picking someone who would carry out his own wishes without really striking out on his own. When he found out that he was wrong, he became upset and ran against Taft in 1912.