If your parents had foot problems, it doesn't mean that you will have them too. It just means you should take especially good care of your feet in order to prevent them.
Seventy-five percent of people will have foot problems somewhere during their lives, so chances are high that you will too. Much can be done to prevent foot problems, the most important thing being the right choice of shoe.
Ill-fitting shoes can lead to severe foot problems, which include corns, calluses and bunions - all of which you can get even if your parents had no foot problems at all.
But if your parenst did have foot problems, you should make proper footcare a priority in your life.