Why should greyhound racing continue?

Sure, why not? It's not the racing itself that is a problem in most cases, it's the way the dogs are treated by their trainers and owners.

Greyhounds love running. They enjoy it. Many racetracks treat their dogs really well and the dogs are happy.

Of course, a controversial aspect of Greyhound Racing is the danger of such races. Yes, they can hurt themselves but it's similar to an extreme human sport. But dogs hurt themselves all the time playing too.