If there's no way to instruct someone how to do something, either the thing or the person might be described as unteachable. Some people think that a sense of humor is unteachable — you're either funny, or you're not!
While some subjects and concepts can be taught, others — the unteachable things — just can't. Math, grammar, and how to brush your teeth are all teachable. While not everyone agrees on what qualifies as being unteachable, some believe that talent and personal qualities like empathy, common sense, patience, and charisma fall into this category. Occasionally, a person may be described as unteachable, but this gives short shrift to the abilities of all humans to learn if they're taught in a way that works for them.