Absolutely not.
There are two major reasons people lose their teeth: severe tooth decay and severe gum disease.
There are three big risk factors for tooth decay: diet, hygiene, and genetics.
There are two big risk factors for gum disease: hygiene and genetics.
So you can see that your oral health is influenced by your parents' genes. However, and I want to be clear, the risk factors that are under your control are more important. You could have the best dental genes in the world, but if you eat a high sugar diet and fail to clean your teeth, then you're very likely to get cavities.
No one is predestined by their genes to lose their teeth. Good home hygiene, a healthy diet, and regular visits to your dentist will help you keep most or all of your teeth for your lifetime.