For every inch of growth I get, I get the same amount of breakage, so my hair never gets any longer. What could this be?

 Your hair may not have enough moisture in the strands. You may need to deep condition your hair at least weekly. Or, there could be excessive stress in your life. Stress dries out your hair and skin. Also there may be chemical changes in your body such as menopause. Other factors that affect hair growth are birth control pills, immune deficiency, changes in medication, heavy medications, lack of important vitamins and minerals, poor dietary choices, excessive coffee drinking, excessive alcohol drinking, cigarette smoking, rough combing, using hair products that strip natural oils from your hair, not washing your hair on a regular basis, chlorine from the swimming pool, certain no-lye relaxers, bleaching and dyeing the hair frequently, applying a relaxer over an older relaxer instead of just the new growth, or leaving a relaxer on your hair too long. You will need to examine your hair regimen and lifestyle to determine which of these is contributing to your breakage and take steps to address the issue.