Wow, I'm a little late to this, but I'll jump on in.
Before I reveal why gay people want the right to get married, I should probably take a moment to make the definitions in this issue very clear.
1. Marriage is a civil right, defined as such by the U.S. Supreme Court in the 1967 Loving vs. Virginia case. The court specifically stated: [i]Marriage is one of the "basic civil rights of man," fundamental to our very existence and survival.... [/i]
2. Marriage is not a religious institution. Every government requires two people to acquire a license to get married, but it does not require those people to have a religion. Marriage existed long before religion did.
With those two factors clearly and irrefutably defined, I can tell you why gay people are fighting for the right to be legally married. When a man marries a woman, it grants that woman the legal status of "NEXT OF KIN." Marriage legally unites two individuals as family, thus giving them all of the rights and protections of a family member. This is a status that CANNOT be granted by a durable power of attorney nor by any other contract or legal document (aside from adoption of a child).
Here is another factor that compels gay people to fight for the right to get married (instead of accepting civil unions): Marriage is incontestable (in other words, no authority can tell a legally married couple that their marriage is not legitimate) in every state; civil unions lose their legality in states that do not allow them.
You see, it really is about civil rights, because marriage is a civil right. It is being denied to gay people based on gender, which is the definition of discrimination.