Wrong, the 16th amendment authorizes the income tax, but the progressive rates would violate equal protection under the law. Everyone should pay the same rate.
Not that I agree that the Constitution says that because the law is based on income so if you make $X, your tax is X% and everyone abaides by that law. Just like the marriage law is man and woman. Even gays have the right to marry someone of the opposite sex.
No court has ever made any ruling remotely close to that, and since the first income tax authorized under the 16th amendment was progressive, it would be hard to argue that the original intent of the authors of that amendment wasn't to authorize progressive taxation.