Handstands allow you to see the world in a new way. If you have been upright nearly every moment of your life and then you are upside-down — well, that feels different. Your body experiences space with a new orientation. That experience alone is a worthwhile endeavor, because seeing the world differently for a minute can sometimes put the right-sided world in perspective.
The other thing is this: Handstands are fun. They open up your shoulders, rush the blood to your head in a wonderful way, and provide a terrific core challenge. The feeling of steadying yourself with your hands, your body stretched out glorious above you, with legs long and straight, or bent or split or in a stag — it is freedom of movement, and you are unhinged in the best possible meaning of the word.
I contend that most people can learn to do a handstand. You need strength in your arms and core, but not as much as you might think, especially if you have a wall behind you to kick up against. (I definitely recommend a wall until you understand how to fall out of a handstand without landing on your bum.)