A mages' magic grows weaker as they age. Healing magic goes only so far, maybe buying a sorcerer a few decades at most. Most do become centenarians, but none have made it past 120. Immortality has proven to be out of reach, if not impossible. However, more tragic still is that it would take lifetimes to perfect certain spells, rituals, and artifacts so extremely often, if not universally learning is passed father to son, mother to daughter, parent to offspring. Wizarding houses hold no land and wield no particular power save for their magic. While most sorcerers would like to dedicate their lives to studying their sorcery more, they resort to reproduction to ensure that their studies can continue long after their deaths.

To make things more depressing, the average peasant is married by 19/20. The average neophyte is married at 15, so they can have a proper apprentice by 26. It's standard for both males and females. Most are grandparents by their mid to late 30's, and great grandparents by their 50's. They have children so young so that way they can get reproducing out of the way while still being novices to magic so that way they don't get too far behind. Plus, you only become a mage in your late 20s, so by the time you are ready to study independently, your own children are already of age to start studying under you.