First and foremost, the Chaotic Neutral character is an individualist who is interested only in their own freedom. While they value liberty, it is their own, and they are often uninterested in supporting the freedom of others. They reject tradition and authority of all kinds, simply because they can, but they do not usually act to topple lawful systems, either.

Even if a Chaotic Neutral character is unpredictable, this does not mean they don't follow any internal logic or act randomly. They can, of course, but the typical Chaotic Neutral character simply just wants to do what they want, unrestrained by any sort of system.