There are many points that you could bring up in an essay on this subject.  Among them are:

• Equal rights.  You could argue that people should not be discriminated against simply because they want to marry someone of their same sex.  Gay marriage, you could say, is nothing more than a part of giving people equal rights.
• Law should not be driven by religion.  This is a point you could make to refute one of the major arguments against gay marriage.  You could argue here that the main reason to ban such marriages is that they are against traditional Christian morals.  You could say that it is not right for the government to enforce the moral beliefs of a particular religion.
• Gay marriage is actually good for society.  Here, you could argue that society benefits when people remain in committed relationships.  If family is the basis for society, shouldn't we want more people to be in stable families?  Allowing gay marriage would be a way to promote this.

If I were writing a 5 paragraph essay on this issue, these would be my three main arguments.