Where in the constitution does it say the USSC is the final determinate as to what is or is not constitutional? Nowhere. There is a reason early presidents told the USSC to pound sand. They were following the constitution.
Actually, it was taken as a given by the founding fathers as judicial review in the state courts, for their state constitutions, was used even before the US constitution, and no fewer than seven of the delegates to the constitutional convention had been state judges or lawyers directly involved in that type of constitutional review.
But that was further cemented by from both Article III and the Supremacy Clause of Article VI, phrased in such a way as to make this an implied power of the SCOTUS, and such subordinate federal courts as congress created.
And it is entirely logical, as it means they have to explain their judgment. Were it not to determine constitutionality, court cases would be beauty contests just based on the personal opinions of justices.