Question: Where does the concept of the House selecting their Speaker come from?

The House of Representatives shall chuse their Speaker and other Officers;
(US Constitution, Article I, Section 2, Clause 5)

House selection of officers - George Sweeney

The concept of the Speaker of the House comes from the British House of Commons. Even though the House of Commons elected their own Speaker it required concent of the Crown.

In the "Colonies" the legislative assemblies also selected their own Speaker but the Governor, that was appointed by the Crown, had the power to reject their selection. When the Colonies declared their independence they retained the office of Speaker in the House, but rejected having their selection approved by someone outside the House.

During the Constitutional Convention the delegates looked to the Massachusetts Constitution of 1780. Their constitution states: "the House of Representatives...shall choose their own Speaker, appoint their own officers, and settle the rules and order of proceeding in their own House." This provision supported the concept of separation of power. This gave the House independence from the executive and judicial branches of government as well as independence from the other body of Congress, the Senate.