It always depends on they way you decide to present this information and the timing for your explanation. From what I understood, the reason you want to use your family history as an argument is to to demonstrate the strong calling you feel to have chosen education industry.
There are a few considerations depending on the format of the question and the context. Here are some scenarios.
Cover letter. Make sure it sounds more like "I really believe in education" rather than "My family has been in the industry and it's comfortable to me". You can do so by making your motivations more important than the fact that your family has been teaching for generations.
Online form. Most recruiters will only be spending seconds scanning your answers. It's best if you go straight to the point. "I consider that education can make a positive impact in people and I feel a strong vocation towards teaching".
Personal interview In my experience performing interviews, this is the space to explain your motivations a little further. This is where you can really show that enthusiasm because you can count on non-verbal cues to communicate. Again, make sure you state your personal motivations and only use the family history as an insightful fact.