Supreme Court and the 14th Amendment

In Brown vs. Board of Education, the majority opinion was that segregation was bad because of the negative psychological impact on the people who experienced segregation.  In this video, a pediatrician and father addresses the issue of whether there is harm caused by same-sex marriage.

This month, the Supreme Court is set to hear Hollingsworth v. Perry, which challenges the constitutionality of Proposition 8 in CA, which banned gay marriage.  An argument of the petitioners and of the White House is that Prop 8 does not provide equal treatment under the law, which would be an argument that it violates the 14th Amendment.  How might claims about psychological harm impact this court decision? Read an article about this here.