You may have misconceptions about “do greyhounds make good pets”. These dogs are bred to be a hunting dog, with features that are slick and aerodynamic in order to offer speed, and independence that results from chasing animals without any sort of human interaction. This breeding has resulted in personality quirks for the breed, which include the natural drive to chase. The other animals in you area will be tormented by the greyhound if it is allowed out without a leash.
This breed of dog will also instinctively fight being confined. Their need to chase will lead to the dog giving chase to anything that moves very quickly. This includes animals, running kids, anything. The best safeguard is to always use a leash.
Training will not remove genetic behavior. Despite all of this hunting instinct, the greyhound is surprising in its laziness. They are pretty submissive and calm, and quite the lounger. They will have loving personalities and are capable of following commands pretty well, unless they are in the mind to chase something.
This surprising behavior is a result of breeding for rapid releases of energy. They are meant to spot, give chase...