His comments fly in the face of 40 years of Supreme Court precedent. Since the 1971 case, Reed v. Reed, it has been clearly understood that the 14th Amendment prohibits discrimination based on sex. In decision after decision, many authored by conservative Supreme Court justices, this principle has been reaffirmed.
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Scalia's views are extreme and out of step with the mainstream. He says that nothing in the Constitution prohibits discrimination against women; rather, it is up to legislatures to ban discrimination if they so choose. However, the Constitution provides a safety net to protect against the will of the majority when fundamental rights — such as the right to equal treatment — are at stake.
http://www.aclu.org/blog/womens-rights/constitution-pro...