The Mayo Clinic gives some very good reasons why you should train for strength. The programming recommendations are less than optimal for gaining the most strength quickly, but it is at the very least good to see the organization moving in the direction of strength for all ages.
Osteopenia and osteoporosis are problems that confront many people, especially women, as they age. Both conditions are essentially an increase in fragility of bones. This is why falling down as one gets older my be a catastrophic event. In the link below Dr. Anthony Komaroff a physician and professor at Harvard Medical School answers a question regarding osteopenia then goes on to explain how strength training works to treat and prevent these afflictions. I have personally had two occurrences in the last year that provide opposite ends of the spectrum relating to this. The first is my mother, who has been training with me for nearly two years. She is 65 and fell onto her hip a few months ago. Happily all she received was a significant bruise but no damage to her bones. The second is my uncle, who was quite a bit older (pushing 90) did not strength train later in his life. He fell and broke his hip, within five days of surgery to fix it he was sent home to recover and died. Realize I understand they have different circumstances but that’s sort of the point. Had my uncle been told to lift weights he’d probably have not needed to hip surgery and would have had a higher quality of life. My mother has I high quality of life now and will continue to have an independent for a long time because of the time she is investing now.