Does brushing hard make your gums recede? (cervical abrasion)

Yes, scrubbing hard from side to side can cause cervical abrasion - a notch worn into the neck of the tooth - along with gum recession. The worn area is sensitive to cold water and to brushing, and once the gum has receded and the tooth has been worn away, neither recovers on its own. The correct approach is 1) use a soft-bristled brush, 2) use the rolling method, sweeping from the gum toward the tooth, and 3) hold the brush lightly, as you would a pencil. If an already worn area is sensitive it can be restored with resin, and if the notch is deep and close to the nerve, root canal treatment may be needed, so please have it examined.