The answer to this question is rather complex, as both sides of the argument about horse racing have thoughtful, passionate arguments. Whether or not horse racing is inhumane depends on many factors, including the type of racing under discussion, the horse, and one's own beliefs about cruelty to animals. Ultimately, it is a decision people have to make for themselves, although a growing number of reformers pushing for changes in the horse racing industry seem to suggest that some aspects of racing certainly are inhumane.
In some senses, horse racing could be considered very humane. A champion horse is an extremely valuable property, and trainers, owners, and staff will go to great measures to keep the horse comfortable, settled, and happy. The best horses get regular equine massage, affectionate contact with human beings, and a chance to compete with other horses; since these animals are naturally competitive, once could argue that horse racing does not force animals into a particularly unnatural state.
When a champion horse is finished racing, the horse is usually retired to stud, or turned into a broodmare. Horses used for breeding are also very well treated, out of a desire to ensure that they bear healthy, rugged, strong young, and they are often in fact quite pampered. At all times, the horses receive regular veterinary care and constant attention from dedicated staffers.
However, the pampered life of a champion is not available to all horses, and the further down the food chain of the racing industry one goes, the more gruesome this sport can become. Horses with little value are treated more like commodities than living creatures, and they may be brutally run into the ground before being sold for slaughter after they outlive their usefulness. These horses may suffer from a variety of untreated health complaints, and they may also be drugged, beaten, or surgically altered in an attempt to enhance performance, making their existence rather unpleasant.
This sport can also be brutal for mid-range horses which do not make it into the ranks of the champions. A single devastating injury can end the career of a racehorse, putting its fate into question, and of the vast numbers horses sold each year in yearling auctions, only a fraction make it into prestigious races. The rest tend to change hands frequently, typically moving further and further down the food chain at each step.
Horse racing is also rife with many of the issues which plague human sports, including drug abuse, over training, and financial shenanigans, much to the disappointment of people who are involved in the sport out of a love for horses, rather than money. People who wish to see reforms in the racing industry have pushed for more frequent inspections and firmer laws at all levels, from prestigious tracks to county fairs. Many advocates also work in the background to find good homes for injured racehorses, and to show people that ex-track horses can be rehabilitated and used in a variety of equestrian sports.