One element of misunderstanding, it seems to me, is about whether marriage is important. For some people, marriage is viewed as a purely religious/cultural construct which should be dictated by their religion/culture. They don't see why it is so important for gay people (or sometimes other minority groups) to be able to marry. Especially if alternatives such as civil unions exist. They have the privilege of not being denied the marriage of their choice.
In contrast, for many people marriage is a large and practical thing since it can affect things such as immigration status, benefits, hospital visitation, etc. (As well as having their relationships treated as second class in the eyes of the wider society, of course). In my view, it is unfortunate that the practical side of things exists. I am lucky enough to live in a country where marriage is (mostly) not important in that way, and I prefer it greatly.
Marriage is a wonderful thing, and I would not deny it to anybody who wants it. In my view, it should not involve either the state or any cultural or religious institution. I find the fact that a couple has to be married by a third party weird. In my ideal world, the people being married would only have to marry themselves to each other, and no-one else would get a say. Marriage should simply be a public declaration of commitment in front of the people who are important to those being married. No-one should have to officiate or register it, and no-one should have to say who can or who can't get married. And certainly, being married should have no effects on your legal or moral life.
To clarify, I don't think marriage should lead to tax breaks or extra respect from any institution. I don't believe adultery should be judged any better or worse because of it, etc.
Once marriage brings material benefit from the state or the legal system, and once marriage is bestowed by an institution rather than being freely chosen, it becomes just another tool for enforcing established power. By allowing powerful groups of people to bestow benefits either social or material on individuals, it becomes open to corruption. It becomes something minorities have to fight for and which exclusive majorities seek to prevent others obtaining. That an expression of love and commitment ends up like this is immensely saddening, and says a lot about human society.
And don't even get me started about the commercial side of things. The whole wedding industry makes me feel sick.