According to my logic, it's a waste of money since there are so many ways to train your muscles for free.(think running, cycling, training with your own weight, training with heavy objects, you can do whatever your creativity allows you to think of).
Sports isn`t only for training your muscles. It can also be a way to meet new people, get together with people you like and a good way to clear your mind for a while. Sports have a different meaning to anyone. You seem to think that sports is only good for training your muscles, in which case a lot of things will seem as a waste of money. For most people however it is a form of entertainment (as said before in this thread).
The reason people are willing to pay for sports is because for a lot of sports you need a good place to play it. If you want to play tennis for example it is quite usefull to have a tennis court. It is also quite usefull to maintain this court so it stays a playable field. Making a tennis court and maintaining it yourself is much more expensive than joining a tennisclub. Because a tennisclub shares those costs between all members. Besides that, sportclubs often offer extras, like diners or fieldtrips. These often come at a lower cost and they are a great way to be around your friends.
Even when it comes to just training your muscles. You`ll need certain machines to do certain exercises. You can`t train all your muscles just with the everyday object you have at your home. So you`ll need to buy some stuff and you need to have enough space to place all of those machines. This is quite expensive, if it is even possible. So once again it is better to share the costs with others and go to a fitnisscentre or something. There you`ll also be assured that you don`t need to maintain the machines nor need to buy new ones when old ones break.