Why aren't some Koreans/Chinese born and raised in Japan nationals?

It's not because they can't Be Japanese.
It's because they don't want to be.

You may come across an article or two on the internet that draws conclusions from the Korean and Chinese population who were born in Japan, speak nothing but Japanese, have lived in Japan all their life, and may have never visited China or Korea, yet they do not have Japanese nationality. These articles sometimes mistakenly conclude that this is evidence that the naturalization procedure in Japan is either extraordinarily difficult, non-existent, or is prejudiced against certain races or nationalities.

The real explanation has nothing to do with naturalization difficulty but rather choice; for a combination of historical reasons, cultural identity reasons, and political reasons, the class of Korean and Chinese (there are other nationalities as well, but the CK demographic is greater than 90%) who have the unique SoR (在留資格 {zairyū shikaku}) of "Special Permanent Resident (特別永住者 {tokubetsu eijūsha})" post-1985 (the date of the last major nationality law overhaul) are intentionally choosing not to acquire Japanese nationality.

The naturalization process contains specific provisions for SPRs: they always qualify for extra 簡易帰化 {kan'i kika} (simplified naturalization), and they don't have to write the 動機書 {dōkisho} (motive [for naturalizing] essay), among other things, and they don't have to fulfill the naturalization requirement that they be able to make or have a reasonable chance to make a living and survive financially in Japan: they are allowed to be receiving welfare or even homeless & destitute. The rejection rate for modern 1985+ naturalization has always been very low (less than 2%) and few SPRs who inquire about it give up, and Chinese and Koreans still to this day comprise the vast majority of those who apply and successfully naturalize.

The politics behind an individual's decision to do this are beyond the scope of this site, but one could look into the very complicated history of the government that existed in Japan during World War Ⅱ. One needs to consider the forced conscription, annexation and cultural imposition events of history, followed by the complicated histories of Korea/China/etc and their wars and changes of government. These events led some in Japan who were in Japan after the war and formation of today's democratic government to find that their home no longer resembled the country they knew — from either a political, geographical, or nationality perspective.

Another thing to remember is that including Japan, most countries do not allow or limit multiple nationalities to exceptional cases, so acquiring Japanese nationality would mean losing their other nationality.

Why don't they just automatically give these SPR people Japanese nationality?

Some people say they shouldn't even be required to naturalize even though they reduced the requirements to practically nothing for Chinese/Korean/etc SPRs; they should just give it to them without even requiring them to apply for it.

What these people don't understand is that such a perceived unilateral action would actually be extremely controversial and would probably be strongly protested… by the Korean and Chinese community in Japan! Many of these legally foreign residents came from countries that the Empire of Japan forced to Be Japanese and assimilate. If Japan was to again assign Japanese nationality automatically at birth to these people, it could appear is if Japan was assimilating these Koreans & Chinese etc by force to be Japanese yet again just like the Imperial era.

Remember that a nationality is not just a set of privileges & rights, but also a set of duties & responsibilities and an official tie to a nation-state, including a non-optional tie to Japanese law, even when one isn't in Japan, and Japan's Constitution (which defines the Emperor as the symbol of the state) that you can't easily get out of.

Instead of claiming these people by assigning Japanese nationality and making them "opt-out" by renouncing (which would be difficult in that they'd have to secure another nationality before they could do this due to United Nation's Convention of the Reduction of Statelessness), Japan's Ministry of Justice makes naturalizing as easy as possible (as evidenced by the extremely high approval rate hovering near 100% when rounded) for Special Permanent Residents; in essence this creates an "opt-in" system where any SPR that wants Japanese nationality can easily get it. The only SPRs that can't get naturalize are those with criminal records; because of this, SPRs get special protection from deportation.

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It is true that these SPRs have been victims of unfair discrimination and many faced incredible hardships due to past wars. As non-nationals living in Japan for generations, special interest groups exist for these born-and-raised in Japan SPRs that lobby for additional rights for those with SPR status and protect the culture and heritage of those who choose not to become Japanese yet live in Japan forever. However, other than anecdotes, there's no statistical evidence pointing to the modern naturalization laws being discriminatory against certain ethnicities or nationalities or being exceptionally difficult when compared to other countries.

The population of SPRs has been dropping every year. The released naturalization statistics do not clearly indicate if this is because the younger generations are choosing to naturalize, intermarriage with Japanese nationals (which causes their children to automatically receive Japanese nationality at birth†), or like the rest of Japan and other developed nations, the existing population (not counting immigration) is no longer growing. As of less than half a decade ago, regular permanent residents began outnumbering special permanent residents, and Chinese now outnumber Koreans in Japan.

† The 1985 nationality law change was made for many reasons — but one of the big changes, in order to comply with the U.N.'s 1979 CEDAW, was to allow the inheritance of Japanese nationality not just from the father, but from the father or mother. This practically doubled the number of Japanese-at-birth children between Korean and Japanese nationals. Interestingly, some Korean political special interest groups in Japan were against this equality measure, as they predicted (correctly) that it would cause the 在日 {Zainichi} (meaning literally, "residing in Japan", but in popular usage, a shorthand to mean those with 韓国籍 {Kankoku-seki} (South Korean / ROK nationality) or 朝鮮籍 {Chōsen-seki} (Korean pseudo-nationality*), who were born and raised in Japan, population to decline, which would lessen their numbers and hence their influence.

‡ After the former supreme leader of North Korea, 金正日 {KIMU Jon'iru} (김 정일 {GIM Jeongil}; KIM Jong-il), publicly admitted in 2002, after decades of denial, that the DPRK government had used military spies to covertly kidnapped and abducted Japanese adults and children from Japan's sovereign territory, many Zainichi chose to not keep their Korean nationality. Also, special interest political groups and many Korean schools in Japan, especially those teaching and representing North Korean ideology, had trouble raising funds and maintaining enrollment.

* Due to the Korean War, Zainichi who previously held Korean Nationality but became stateless when their unified country ceased to exist due to the division of the country, yet did not or would not choose a nationality from the two new nation-states, were assigned the unofficial placeholder pseudo-nationality of 朝鮮籍 {Chōsen-seki} by the Japanese government for their SPR Alien Registration.