I think part of the issue you have with it is the speed at which some people get married after dating. I don't have any statistics on the issue, but I'd be willing to lay money on the line that the less time a couple spent together before marriage, the greater the divorce chance (and for purposes of this discussion, I'd rule out drunken Vegas marriages completely as they tend to have a 24 hour turnover time). I personally spent about 4 years living together with my wife before we married, and you get to know a lot about a person in that period of time.
The main reason most people get married is to publicly declare how they feel for each other. Most people don't do it for the financial reasons (but they do tend to be a good bonus), and if they are doing it for children, it's usually the "Oops, I screwed up and now you're pregnant, guess we gotta get married" variant which is usually not a good idea. One partner or the other tends to feel resentment about it after a period of time, which will poison even a good relationship. And if they are the type of person who gets in that situation, they also tend to be bad at planning for the future anyways, making an extended relationship harder. I know I'm generalizing a lot, and there are relationships like this that work out, but it's hard not to generalize in this type of discussion.
As for kids, you could start a whole discussion just on that. I personally feel that it is better for the children if the parents are in a good relationship together, married or not. Marriage just helps to answer a lot of legal issues (child support, who the child lives with, what happens if something happens to one parent, which parent to officials like doctors and teachers need to consult about issues with the child, etc.). If the couple is married, or at least living together in a good relationship, either parent has the authority to address any issues. If the parents aren't together, then you constantly run the risk of one parent breathing down your neck about why you did/didn't let little Johnny go on the class field trip, or didn't tell them about some minor accident Susy had.
Is marriage always the right answer though? No. There are many reasons why it is right for some people, most of which were already mentioned (love, children, financial stability, religion, social pressure/tradition, family honor, legal reasons, etc.), but there are just as many reasons why it is wrong for some couples. One of my friends has lived with the same woman for over 20 years and neither of them want to get married. For all intents and purposes they might as well be married, but they (like the OP) don't believe in marriage, and that works for them. I know another couple who have been married to each other three times. Why? Because when they are not married to each other, they are great together. They love each other, want to be together, etc. But the minute they get married, they go at it like cats and dogs. Eventually they learned they didn't need to be married to each other, got the divorce, and settled down together. For some people marriage is a connection, and that's a good thing. For others, marriage is a chain and that's a bad thing.
EDIT: I forgot to mention that I don't think people should stay together just because they have children. If a relationship is not working out, I believe it is better for the children if the parents just make a clean break and come to some sort of agreement on the raising of the children. That way the children aren't stuck dealing with their parents' baggage.
