This is a quick theory I came up with while doing some research.
Conservative arguments tend to be based around some idea of natural laws or a natural order, that there's a way things simply ought to be. They believe that there are rules about how societies should work hardwired into the fabric of reality (according to many conservatives by god, but certainly not all) and that to act against them would be as foolish as trying to break the law of gravity.
Liberal arguments, on the other hand tend to focus on a belief in some concept of natural rights. They believe that simply being born and having humanity entitles every individual to certain universal rights such life, happiness, equality etc.
When it comes to the friction between modern (US. at least) liberals and conservatives, it basically comes down to two different conclusions from each world view. The left now believes that, if left alone, people will naturally attempt to one-up and exploit each other, bringing society farther and farther away from the universal levels of happiness, equality, etc. that people are entitled to. Thus heavy government intervention is required to ensure rights to all. The right, however, largely holds the belief that rights are determined by natural law, and that those who are most good or nice or deserving will tend to end out on top simply because that's the way the rules work. Thus they argue that things will actually run the smoothest with as little intervention as possible. If traditional systems don't always work perfectly fair then conservatives are more willing to accept "Well, it's out of our hands, that's just the way things are." While liberals see every injustice as a completely human error that could have been prevented and a total tragedy.