The biggest problem with growing old is having to deal with loss.
Loss doesn't mean just the obvious of the death of friends and family that most people think of when they think of growing old: most people think of the elderly when they think of "growing old." Loss happens much sooner than those twilight years.
Growing old means you have to accept you can't perform athletically where you used to be able to perform. You're that half step slower, the split second off. You have to become crafty, and wiley to compensate for that loss. That is, if the small nagging injuries don't build up to something much worse in the mean while.
You have to deal with the loss of knowledge. All those equations and facts and formulas and processes you learned in school, the techniques and stories and details that you don't use everyday or at least every week on the job or in your passions, they disappear, to be forgotten. You look at your child's homework, recalling when you learned the same things, and think, "I used to know this." You realize you have forgotten more than you currently know, more than you realize.
Loss means the loss of people around you. Not only the loss of death, for that is the biggest of all losses, but rather, the smaller losses of distance when friends move away, or change. Or the losses that occur when a friend moves on to a new phase of life with weddings and children and promotions. The loss can result from a joyous event, but it remains no less a loss.
You have to deal with the loss of childhood. No longer can you just let someone else just take of you. You've made this life you call your own, and you have to deal with the consequences. Each of your actions has consequences, a fact most people try to forget. Every time you have to be an adult and face your life, you are recognizing the loss of those carefree days when someone else provided food, and shelter, and as much love as they were capable of giving. Many people never acknowledge this loss.
And, you have to deal with the loss of your dreams. At some point, you have to wake up from the fog of not thinking, and realize that you haven't achieved your dreams, that this isn't the way you expected life to turn out, that this isn't what you signed up for when you were a kid, hoping, and dreaming and plotting.
And at that moment you have a choice. You can change. You can fight for what you believe in. You can learn to say no. You can learn to say yes. You can become mentally stronger. You can stop worrying about the little details, the pieces of life that others say are important, and focus on the parts you believe are important.
Or, you can choose to accept the loss of your life. If you make this choice, you've already died.