For reference, the 14th says:
No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
So, that means that a state is forbidden from doing three things:
1) Reducing the rights or privileges granted to people by the federal government.
2) Take away a person's life, liberty or property without due process
3) Exclude people from the protections offered by state laws
Marriage is not a right or privilege granted by the federal government, so #1 is out.
#2 The state needs to prove that they are giving due process under the law, with that process being usable while treating homosexuals differently. becuase of court classification which I will better explain in point #3
#3 is a bit tougher to make. It sounds very clear cut- states can't deny any person equal protection of the laws. But in practice that super clear cut interpretation doesn't really work. For example, a felon can't vote, a young person can't claim benefits designed for the elderly and a person who isn't handicapped can't get a handicapped license plate. States realistically have to be able to control what laws apply to which people to some extent or you just end up with an absurd situation. So, the courts have devised a three tiered system for the characteristics that states could potentially use and different burdens of proof for them:
Strict scrutiny- states can only discriminate if they have a "compelling state interest" and the way they are discriminating is "narrowly tailored" to that state interest. What that means is basically that they need a really, really, important goal and there basically isn't any other way they could accomplish that goal. Virtually no law ever survives strict scrutiny in the 14th amendment context.
Intermediate scrutiny- states can only discriminate if they have an "important state interest" and the way they are discriminating is "substantially related" to that interest. This is basically just a weaker version of strict scrutiny. The state needs to be doing it to further an important goal and the discrimination needs to have something that ties it pretty closely to that goal. Laws often survive intermediate scrutiny.
Rational basis- this means that states can discriminate so long as they have some kind of a rational explanation for why they're doing it. The court doesn't need to agree with that reasoning, they just need to find that the state is acting rationally. Virtually any law will survive rational basis analysis (although not always).
Different characteristics of a person fall into different ones of these categories. Race, religion and national origin are in the strict scrutiny category. The only characteristic in the intermediate scrutiny category is sex. It makes sense to have that there because there are some things that states just need to do to treat men and women differently- for example, separate bathrooms or accommodations for pregnancy, etc. But, the courts also want to be able to prevent flat out sex discrimination. So they keep it in the middle tier and pretty much decide case by case. Everything else is in the rational basis category.
I think I am going to add this to the first post