Question: Why did the Founding Fathers think it necessary to give the House of Representative the power to impeach the president?

The House of Representatives ... shall have the sole Power of Impeachment.
(US Constitution, Article I, Section 2, Clause 5)

Impeachment power - George Sweeney

The Founding Fathers wanted to provide a means in the Constitution for the disciplining a president for abuse of power without at the same time giving the legislature the ability to hampering him from performing his duties. Understanding human nature they knew unfettered power could result in unfettered tyranny. Impeachment can be compared to a Grand Jury bringing criminal charges against some one.

There was concern that members of the federal government would not have the will to monitor each other. From this concern it was proposed that Congress could remove the president upon the request by a majority of state legislatures. However this proposal was viewed subjecting the president too much to the states.

Though Mason and Morris expressed fears that giving impeachment power to the House would empower the lower legislative body to manipulate the president the Constitutional Convention decided to follow the model in England and several states, to give impeachment power to the lower of the legislative bodies.