Japan didn't have a strong tradition of raising animals for meat, until after the Meiji Restoration. There were, at times, legal restriction on the eating of meat, and there were social taboos on eating meat, killing animals, and butchering.

Meat-eating fell into four main groups:

1. Medicinal. Get your doctor to prescribe meat (e.g., beef) as a medicine.

2. Upper-class hunting. The upper classes hunted, and the animals they killed ended up on the table.

3. Low-class hunting. Peasants hunted. Some were officially registered as hunters (as their occupation), and some were peasants who might shoot animals (officially, in order to protect their crops). During the Edo Period, both hunters and peasants who needed to protect their crops (i.e., many peasants) could own guns, and used them for hunting. The animals they killed were eaten.

4. The eta (to use the old term, considered derogatory today, meaning "very unclean") were the outcaste underclass of Japan, who worked in the "unclean" occupations, including butchering. As an outcaste, considered unclean by the rest of society, they could ignore the social taboos on meat-eating.

A key point of all this is that the animals that were eaten were either wild game or animals (at least officially) raised for other purposes. Cattle, raised for traction, and horses, raised for riding, might be eaten when available. Some cattle were raised for meat, with the meat officially eaten for medicinal purposes. Dogs were not raised for meat (unlike the cases of Korea and China). Dogs received further legal protection under Tokugawa Tsunayoshi (the 5th Tokugawa shogun, AKA the "dog shogun"). In 1687, he banned the killing of animals and the eating of meat, and a series of laws protecting dogs, including strays. These laws were promptly repealed by his successor, and wild dogs returned to upper-class tables.

With the Meiji Restoration, meat-eating was encouraging, and this meant that raising animals for meat was encouraged - wild game would not suffice. Cattle, pigs, and chicken were raised for meat, but not dogs. Dogs had been a relatively rare component of the wild game eaten before, and there was no strong motive for continuing to eat dog meat. Thus, meat consumption rose, but dog meat consumption did not. Dog meat was eaten in late 20th century Japan, and into the 21st century - mostly by Koreans living in Japan; this meat was mostly imported from Korea. However, there were ethnic-Japanese customers for dog meat, too.

The West and Islamic Asia are unusual among world cultures for not eating dog (not counting a few exceptional countries in those areas). In Islamic Asia, religious rules against the consumption of dog greatly reduce dog meat eating, and dog meat has been socially taboo (and also often illegal) in much of Europe for a long time. However, dog meat is eaten in many countries in the rest of the world - China and Korea are just two among many, many countries where dog is eaten. Usually, dog meat is only a very small part of the diet, rather than an important source of meat. In the countries where dog meat is eaten relatively frequently, consumption appears to usually be from about 1 dog per year per 30-200 people (Korean dog consumption at its peak was about 1 per 30, although it has dropped since). This is equivalent to about 500g to 75g of boneless dog meat per person per year, based on the meat yield from Korean dogs.

The high end of that range, Korean dog meat consumption in the early 21st century, meant that about 1% of the meat eaten in Korea was dog (making dog meat the 4th most popular meat, behind beef, pork, and chicken). It was also a relatively expensive "special" meat, usually eaten in restaurants specialised in dog meat dishes. This was a historical change for Korean dog meat consumption, since dog had been cheap meat for the poor in Medieval Korea. For many Korean peasants, dog had once been their main source of meat. However, this was in a very low-meat diet, with dog often only eaten once per year, in midsummer. The amount of dog meat eaten appears to have risen in the 2nd half of the 20th century, but because the total meat consumption rose much faster than dog meat consumption, the fraction of the meat eaten that was dog fell. Noting that some people in Korea (in the early 21st century) did not eat dog at all, and many who ate dog had only eaten it on a few occasions in their life, some people who eat dog must eat much more than the average amount.

The highest per capita modern dog consumption appears to be in Cambodia, in terms of the number of dogs eaten per year. However, the meat yield per dog in Cambodia (where most of the eaten dogs are probably quite skinny strays) is probably far lower than that of Korean farmed dogs. Thus, while dog consumption might be as high as 1 per 6 or 7 people per year, the quantity of meat might still be under 1kg per person per year. With total meat consumption below 20kg per year, this is a large fraction of the meat eaten.

Returning to the subject of Japan, Japan is famous for violating a much more widely-held meat taboo than dog: whale meat. Whale, officially fish rather than meat in pre-Meiji Japan, wasn't subject to the common anti-meat taboos and laws. However, whales were not the easiest things to catch before modern whaling technology was developed, and whale meat consumption was not high. Whale meat become more common in Japan in the early 20th century, and eating whale soared in popularity after WWII, due to shortages of other meat. This post-WWII rise in whale consumption was not confined to Japan - for example, whale was eaten in post-war Britain as an unrationed meat (British food rationing continued for many years after the end of WWII). Current whale meat consumption in Japan is much lower than it peaked at, and is currently only about 44g per person per year. In many other places, where whale meat is still (legally) eaten, it is eaten by indigenous peoples, hunted in the traditional manner.

Reference:

Korean dog meat yield estimate is from Ann, Yong-Geun, "The Effect of Dogmeat Eating on Sanitation and Food Waste Consumption 개고기 식용이 위생과 음식물 쓰레기 처리에 미치는 영향", The Korean Journal of Food And Nutrition (한국식품영양학회지) 23(1), 124-133 (2010). http://www.koreascience.or.kr/article/JAKO201021147395409.pub