Students always have difficulty reconciling Myers v. United States (1926) with Humphrey's Executor v. United States (1935). In Myers, Chief Justice Taft forcefully held that the President has an absolute removal power of a postmaster. But Humphrey's Executor held that the President could not remove a member of the Federal Trade Commission without showing cause. Superficially, at least, there are ways to line up the precedents. The postmaster only exercised executive power, while the FTC member exercised "quasi-judicial" and "quasi-legislative" powers, whatever those are. But there is another explanation I usually tell students.
Humphrey's Executor was argued on May 1, 1935, and decided on May 27, 1935. Schechter Poultry v. United States was argued on May 2 and 3, 1935, and decided on May 27, 1935. Coincidence? I think not. Both of these cases were repudiations of President Roosevelt's powers. Humphrey's Executor unanimously upheld the so-called independent regulatory agencies, and Schechter Poultry unanimously halted the National Industrial Recovery Act. This was not a good day for President Roosevelt. Both cases were largely seen as repudiations of FDR's overreaching powers.
Of course, if Roosevelt lost the battle on May 27, 1935, he would win the war in 1937. Even though there was no actual "Switch in Time that Saved Nine," West Coast Hotel v. Parrish (1937) signaled that the Supreme Court would no longer stand in Roosevelt's way. And, over time, Roosevelt would make nine appointments to the Supreme Court. The rest is history. In a fairly short period, Roosevelt radically altered the Constitution, the Supreme Court, and our republic.