Why did the authors of the Constitution require the approval of the President, the head of the executive branch, before a bill could become a law?

for checks and balances.

Explanation:

Check and balances is a system that we implemented within our government to prevent one branch of the government from becoming too powerful.

The President is part of the executive branch, and the law is created by the congress which is a part of the legislative branch.

By creating a requirement of approval, the constitution provided a way for the executive branch to limit the power of the legislative branch. The president have the power to reject a legislation by the congress if the president believe that the legislation will not be beneficial for the citizens.