I think many Europeans and other Caucasians dislike Japan when they hear that Japanese eat whale meat. These Europeans do not include Norwegian and Icelander who eat whale meat too. Then, also Basques had a long tradition to capture whales offshore and eat them too. United States are against whaling but the US was whaling in 19th century as you can read from the American author Herman Melville's most famous novel, Moby-Dick.
May be US was not interesting in eating the whale but US ships were capturing thousands of whales per year, not only around United States but around the globe. Their reason of the whaling, whale hunting was to get the oil from the whale. After extracting the oil, they dumped the remains to the sea. On the other hand, Japan used everything what can get from the whale.
Whale meat was popular meat in Japan especially after WWII, but declined gradually and rapidly declined after 1987 when commercial whaling was banned. Currently whale meats cannot be found in every supermarkets throughout Japan, and not easy to find in Tokyo either. However it can be found easily in certain regions which have long tradition of eating whales.
Finally the taste. It is definitely not a fish. Then, not a chicken or turkey. Due to whale is mammal, it is closer to beef or pork, but I would rather say that it is closer to horse meat.