law abiding means “not the kind of person who breaks the law,” which is why we have the words “law” and “abiding” in our names. It is meant to be used in a vague way. For example, a person who commits a crime in his or her name, rather than in a law enforcement sense of the word.
If you are a person who just breaks the law in this vague sense of the word, then you probably aren’t a law abiding person.
The definition of law abiding is a loose term, and as such, it can never be exactly defined. However, when someone says a person is law abiding, that person is saying that he or she is a person who has not broken any laws. Some people just break the law. A person who just breaks the law in this vague sense is still a person who is breaking the law.
The term law abiding is also sometimes used in a somewhat more concrete sense. For example, the US Supreme Court defines law abiding as a person who “does not violate the law while violating others.