In the case of JEB v. Alabama ex rel. T.B. (1994), the U.S. Supreme Court ruled that peremptory challenges based on gender were unconstitutional. Specifically, the Court concluded that using peremptory strikes to remove potential jurors based solely on their gender constituted a violation of the Equal Protection Clause of the Fourteenth Amendment.
Therefore, the most likely reason the justices ruled as they did is:
Peremptory challenges on the basis of gender were a violation of the Sixth Amendment.
(Note: The stronger basis for this decision is likely grounded in the Equal Protection Clause rather than the Sixth Amendment, but from your presented options, the closest fit pertains to the violation of rights related to gender-based challenges.)