What do William Howard Taft do do that encouraged Roosevelt to form a new party and run for president again?

The conservatism of Taft was the main reason for Roosevelt to split and run for the presidency again.

Explanation:

Theodore Roosevelt and William Howard Taft were close friends but, the thing that separated them from each other was, their thinking. When Roosevelt became the President of the US, he brought out many progressive policies, and most of them passed in Congress.

On the other hand, William Taft had exact opposite thinking, he was a man with conservative thinking and limited himself to this particular approach. He became the US president but, his conservative ideas were against Roosevelt's thinking, and due to this, Roosevelt chose to split and form the Progressive Party and run for the presidency.