Why would a health insurance company deny new coverage to someone because of past infertility?

Pre-existing: Pre-existing conditions are often used to deny benefits you can try to have a clause written in your coverage to exclude fertility therapy.

Have right to appeal: Many plans cover infertility diagnostic tests, some (depends on employer, plan, state in which the insurance company is based) cover fertility treatment and/or drugs. Many have lifetime dollar limits and other specifications like you have to do IUI cycles before ivf. Coverage is high in a couple of states with mandates. Denial for pre-existing infertility is harsh, try appeal process. Best wishes.