To give a short and simple answer to your question, that is why. The idea of no-surrender can be traced back to the Samurai and the ancient Bushido code, where Samurai would swear everything and their lives to their Lord or Master, including dying for him.

The code commonly seen in WWII took its roots in the 1930s, where the Emperor was given his place among the people as their literal God, and it was viewed as an honor to give one's life for him. More so, the "Senjinkun military code" (or "Instructions for the Battlefield") was a code book given to all members of the Imperial Japanese Military in January of 1941. It is where the quote "Never live to experience shame as a prisoner" was taken from, and lived by. Japanese forces saw it as their duty to die for the Emperor, so as not to bring shame to their family, even when out of ammunition and even without guns. For an example of both, look at Kazuo Sakamaki, the only survivor of the Japanese midget submarine attacks at Pearl Harbor, and how disgraced he and his family was treated when Japan learned he had been captured, even though it was against his will. The other would be found in James Bradley's book "Flags of our Fathers", where it was recorded that a group of Japanese soldiers rushed the Marines atop Suribachi when the flag was raised, and after being cut down, were found to have no ammo, semi functional guns, and even a broken sword. At Iwo Jima alone, out of around 21,000 troops garrisoning the island, only 216 surrendered, with everyone else dying. A point of interest when talking about the Japanese's ferocious fighting spirit is the list of Japanese holdouts, or those who didn't surrender, is rather longer than one would think, with the last one, Teru Nakamura, being arrested in Indonesia in December of 1974. However, that was uncommon, with death in battle or suicide being preferred.

Another answer to your question could be the above, coupled with the dwindling resources, armament, and logistical supply of their forces, as the war progressed. For instance, take an island like Rabaul, which the Allies completely bypassed, instead attacking it from the air and mining the island, turning it into a useless fortress. Allied weapons were vastly superior to the Japanese as the war progressed, with semi-automatic rifles, better planes, and the ability for every naval invasion and ground assault to be opened up with a bombardment, while at times the Japanese couldn't even muster counter battery fire at certain times. Their hopeless situation surely pushed them to a mindset such as the one you asked about

In short, what you've heard is true, with an amazingly strong spirit, coupled with a strong belief system, turning into one of the most highly motivated fighting forces the world has ever seen.

"Casualties" means anyone killed or wounded. There were about 101,000 American casualties in the Ryukyu campaign. Even at the highest estimates, there were about 150,000 Japanese casualties. That's a pretty reasonable ratio for a losing side. The real difference is that 75% of American casualties were not killed and merely wounded. A shockingly small 13% of Japanese casualties are reported as merely wounded. The vast majority were considered dead or missing. That's what I'd really like to see explained. Are Wikipedia's figures accurate there?