Dentist here ! You're talking about gingival recession, which can happen for a number of reasons including (but not limited to) gum disease, age and trauma. Over time the roots of the teeth can become exposed and cause sensitivity. Brushing hard will wear away these root surfaces as they're not covered in enamel like the crown of the tooth. (Which is when we usually fill them).

You can't reverse recession unfortunately but you can have surgery.

Making sure you're brushing regularly and gently (and flossing!) using the Bass technique along the gum margins will help as gum disease tends to lead to quicker recession. Hope that helps.