When the Constitution was being written and debated, the framers clearly wanted to break from the British political tradition of investing all war powers in the executive (the king), but they also knew that legislatures could be dangerously slow to respond to immediate military threats. So instead of granting Congress the power to “make” war, as was first proposed, founders like James Madison changed the language to “declare” war.
Madison was no fan of executive overreach—“the Executive is the branch of power most interested in war and most prone to it,” he wrote to Thomas Jefferson—but that change of wording in Article I, Section 8 of the Constitution implied that the president, as commander in chief (Article II, Section 2), retained certain powers to “make” war, if not declare it himself.