Martial arts training takes what you have and teaches you to get more out of it. It does not teach you how to defeat any old person you may meet. As a result, you will increase the range of people that you are able to defend yourself against, but that range will still have limitations based upon your size. That small children cannot overpower grown men is not very disturbing to most people. What is disturbing are the implications.
Women also suffer severe disadvantages against adult men even when size is equal.
Males have a higher muscle content in their body weight. That means that a 150 lb. Likewise, the 150 lb. The sad reality for the millions of skinny, small, weakling men and women that populate karate schools is that karate, while helping them get more with what they have, cannot help them overcome the reality of physics. A 150 pound woman who earns a third degree black belt in a school of hard training in miilitary arts will have a higher probability of successfully defeating a male attacker than she would have had before the training.