The core belief of sovereign citizens -- initially, anyway -- is the notion that since government exists at the consent of the governed they can "opt out" of being subject to the laws of wherever they are.

This has a tiny grain of legitimate logic to it, in that not a single person on Earth is given a choice of society and/or country to be born into. Governments attempt to exert absolute authority over everyone within their spheres of influence regardless of what those people may happen to think of the matter, and the feasibility of them physically leaving said society/country notwithstanding. All laws are just words on paper, after all, and from a certain perspective completely artificial, arbitrary, and transient.

Where it all breaks down is that these people typically arrive at the above conclusion by being absolutely stark raving loony, and typically want to have their cake and eat it, too -- they don't want to be subject to obeying laws, or paying taxes, or having to register their vehicles and get driver's licenses, pay child support, etc., but they still somehow feel entitled to the use of public infrastructure like roads and bridges, police and fire services, municipal water and sewer use, and so forth. In modern times a simple "no gubmint can tell me what to do and I'm answerable only to myself" outlook has mutated into this arcane and nebulous pseudo-religious willful misinterpretation on the wording of laws, what is and is not printed CAPITALIZED on various government documents, and fixation on "contract law," treating every interaction between everyone and every thing as a "transaction" which the sovereign citizen believes is inherently negotiable (always in their favor, of course).

This is furthered by shucksters who sell books and seminars to ~~idiots~~ the types of people who have the right type of chip on their shoulders, which purportedly contain the secret knowledge and legal incantations to make all this work but are, of course, just bullshit. Usually people who entangle themselves in SovCit bullshit are trying to weasel out of of some particular financial obligation. Not wanting to pay child support seems to be a very popular one, as are taxes in general, fines, loans, and liens.

The whole thing is just fascinatingly whacked the more you look into it. Here's the RationalWiki article on it, for instance:

https://rationalwiki.org/wiki/Sovereign_citizen