Why Haven't Humans Tamed Deer?

Humans successfully tamed and domesticated horses thousands of years ago, but we have not been able to tame deer, which are much smaller and meeker than horses. What is it that makes deer so hard to tame?

In the book GUNS, GERMS AND STEEL, author Jared Diamond lists six criteria that an animal has to meet in order to be able to domesticate, and deer fail miserably in one of these criteria:

Criteria	Deer	Result
Animal cannot be a picky eater	Deer have a varied diet ranging from nuts and corn to leaves and grass, that are almost always available around human residences.	Pass
Animal must to be able to breed in captivity	Deer can be bred in captivity.	Pass
Animal must reach maturity quickly	Deer live an average lifespan of 5 to 10 years and reach maturity quickly.	Pass
Animal must be docile by nature	Deer are one of the most docile creatures on the planet.	Pass
Animal cannot have a strong tendency to panic and flee	Deer have to be alert 24/7 in order to survive. Their only defense mechanism against predators is to flee at the first sense of danger.	Fail
Animal must conform to a social hierarchy	Deer live in herds.	Pass