In the case of JEB v. Alabama ex rel. T.B. (1994), the Supreme Court ruled that using peremptory challenges based on gender was a violation of the Equal Protection Clause of the Fourteenth Amendment, not the Sixth Amendment. The case specifically addressed the issue of gender discrimination in the jury selection process, as the prosecutors dismissed male jurors in an effort to create a more favorable jury composition for their case involving child support.
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.
While this statement does not reference the correct constitutional ground, it reflects the essence of the ruling regarding gender-based peremptory challenges. It is important to note that the ruling was grounded in equal protection principles rather than exclusively within the context of the Sixth Amendment.