We all know there are a ton of celebrities who have generations of stars in their family trees (the Paltrows, Barrymores, Douglases, etc.). Because they grew up around acting, many were probably encouraged at a young age to participate and already had a foot in the door.
I think there are a couple of reasons people follow the same career paths as their parents. It may be that they grew up around it and feel more comfortable with something so familiar, or it could be that parents encourage their kids to acquire certain skill sets similar to their own. It's probably a combination of things. I didn't follow either of my parents' footsteps; what about you?