The determination of qualifications to instruct in martial arts depends on what the collective experience and knowledge is of he/she who makes such a claim.

Many well known martial arts systems have some form of governing structure that provides a reference point in terms of measuring consistency of training and technique as well as determining whom is actually qualified to teach. However, there are many martial arts which have no recognized body regulating them outside of the immediate teacher/student or parent/offspring dynamic. This is how many have actually been able to maintain the essence of what is being taught, while encouraging the individual growth necessary to ascend to the journey of mastery.

In either case, it's typically not a question of simply proclaiming one's self an instructor. One typically has to be recognized by those whom are recognized as having attained some level of mastery, and is typically done in writing. However, as of late one finds many whom, after years of study in many different arts have formulated their own expressions of classical martial arts and distilled them into abbreviated groupings of principles and techniques (typically mixing various combinations from assorted disciplines) and giving it their own label. Most times the information is simplified for ease in training those with no experience. Many of these individuals are known and proven to have attained instructor/sifu/guro/sensei status within several styles already and draw upon these in their re-formulations thereof. They obviously have credentials in classical forms to draw from.

There are those, however who cannot lay claim to mastery in the more classical forms, but have abundant amounts of practical combat experience to draw from. One will often find active or former military and law enforcement personnel as well as others in high risk, and potentially violent occupations (bodyguards, bouncers, professional fighters like boxers, kickboxers, K-1, UFC competitors and other mixed martial artists and others) who will come forward as experts in brutal fighting techniques. While they typically are not recognized masters according to any recognized, classical martial arts entity, they can boast real-life expertise and bring the added element of high stress to what they teach.  One will typically find these individuals teaching reality-based self-defense, as opposed to "martial arts," as training in classical martial arts typically involves education on the base cultures and history of said disciplines, as well as some form of health and spiritual enrichment.

Either way, the road to qualify for teaching others involves paying dues in long and consistent training and experience...no matter what the discipline. This is what determines whether what you have to offer is actually beneficial or harmful to those you teach. There are those who say that "a little knowledge is dangerous," and this is especially true for martial arts, where control and discipline are paramount.

It is said that the novice is far more dangerous than the master because he/she hasn't attained the same level of control, much like a toddler with a handgun...if you can imagine that.