Why can't I call myself “a Japanese”?

"Japanese" is definitely a noun, so it's not grammatically incorrect to say "I am a japanese", but it does sound weird. This is probably related to idiomaticness. In the US, usage of words like "an american", "a canadian" and "a mexican" as nouns generally "sound" ok, as far as popular speech goes, whereas "a british", "a french" and "a spanish", for example, sound strange despite being grammatically correct ("A german" and "a korean" sound a bit weird too, FWIW). As far as I can tell, countrymanship nouns are mostly used with definite articles (e.g. "The japanese participated in WWII"). In other contexts, the rules are mostly based on idiom popularity, if not completely arbitrary. "New yorker" sounds perfectly fine as a noun, but "a san franciscan" is something not many people would ever utter, even in adjective form.

Similar discrepancies can be seen in other noun groups, for example "a beer" is fine, "the wine" is fine, but "a wine" sounds weird.

For the cases where usage of the word as a noun isn't considered idiomatic, people usually say "a korean person" or "a german guy" or "british woman", etc.

"A Japanese" or "a Chinese" were common in English a few decades ago. This has declined very significantly. Interestingly, people often use these as self-descriptions (I think especially non-native speakers).

There is a similar phenomenon with "a Jew", which was once common and where now most speakers would use "a Jewish person" (except, to some extent, for Jews using it as a self-description, although "I am Jewish" is more common than "I am a Jew", but their denotation is also different because the former foregrounds religious identification and the latter foregrounds ancestry or ethnic identification).

Apart from the "person-centered language" phenomenon that other people have mentioned, I think there's the closely related euphemism treadmill

https://en.wikipedia.org/wiki/Euphemism#Euphemism_treadmill

where even a completely neutral term may acquire a negative connotation because of its widespread use in a negative sense, or by people intending to give it a negative connotation. Or people may simply fear that a neutral term has acquired a negative connotation by recalling that it was widely used in the past.

As other commenters have pointed out, there are still demonyms which are common to use in the singular and their idiomaticity has tended to change (mostly in the direction of stopping).

Although I think there's an interesting phenomenon where new countries' demonyms feel plausible to me in the singular ("an East Timorese", "a South Sudanese", "a North Macedonian", "a Kosovan"/"a Kosovar"). It's hard to prove but I suspect that the relative novelty or unfamiliarity of these terms acts to alleviate speakers' internalized fear that they might inadvertently be using the same terminology that was previously used by xenophobes!

But I'm not totally confident in that.

It would be interesting to gather more data by surveying a lot of native speakers about a lot of demonyms and trying to quantify the possible influences of (1) familiarity, (2) phonology, (3) history of ethnic conflict, ...

Another one that feels kind of parallel is the arbitrariness in whether you use a definite article in the name of a country. For example, "the Sudan" and "the Ukraine" used to be very common in English but it's not unusual to see the country names without the article now. On the other hand, "the United Kingdom", "the Netherlands", and "the Maldives" are still always "the". This is different in other languages, where for example "Switzerland" is never "the" in English, but is always "the" in German ("die Schweiz"); "Japan" is never "the" in English, but is always "the" in Portuguese ("o Japão"), as is Brazil ("o Brasil"). It's challenging, though maybe not impossible, to give a clear account of the origins of all of these distinctions...

Edit: in Arabic, too, some countries are "the" and some aren't, but it also doesn't correspond with English practice.

One thing, as the other commenter alluded to: Japanese in US English is almost strictly an adjective, for some reason. Really, any other ese too, including Chinese.

It doesn't sound abnormal to call someone a Korean, or most of the 'an's. But it does to call someone a Chinese/Japanese, as it's only used in the adjective form. We used to have noun forms, but they were deemed offensive long ago - so I'm not sure what the correct way is today.

I'm not so sure about the "offensive" angle - it could be the other way, that is, first Japanese as a noun stops being used (for some reason), and then because of that, using Japanese as a noun starts to sound weird, and then offensive.

Americans have had plenty of racist/hostile opinions against Mexicans or Russians, yet "a Mexican" or "a Russian" remains totally fine.

I think you’d find less confusion if you said “I am Japanese”. It’s not clear to me that “a Japanese” is wrong, it’s just not something I’ve heard before in terms of English phrasing. Similarly, I would likely say “I am Korean” rather than “I am a Korean”.

I've never thought about this before, and it is strange.

From the Wiki article on demonyms though, "Often, demonyms are the same as the adjectival form of the place, e.g. Egyptian, Japanese, or Greek."

I guess you'd also not say "I am a Japanese", but probably just "I am Japanese"?

Similar to how native Japanese speakers often drop particles from their speech, it sounds more natural to say "I'm Japanese" rather than "I'm a Japanese". BTW I'm not American, but Australian. "I'm Japanese" sounds fine to me.

This is because of the "-ese" ending.

For country names ending with "-ese", it's usually an insult to call someone "a" something, like: Chinese, Japanese, Lebanese, Portuguese, or Vietnamese.

With these countries, it sounds better to say "I am from X" or "I am X", such as "I am Japanese".

It has a vaguely racist or offensive feel to my native U.S. English speaker ears. I don’t know why but it does.

In Spanish no one cares if something is a noun or a proper adjective.

There is "chino, japones, italiano, frances, aleman". Full of different Romance suffixes and we put functionality over ideology.

Too lazy to care, and the noun/adj. roots and suffixes go back to the Latin spoken since the Romans.

We have "ingles" and "britanico" too, yet no one would say a common used demonym can be racist.

Also, hey, any demonym can be used either as a noun or an adjective. Both for people and for things.

It sounds racist, even if you say it about yourself. Liberal thinkers are worried about depersonalizing via language so they use phrases like "they are X-ese" or "they are an X person". While the phrase "they are a X" is considered a more derogatory tone that replaces someone's person-ness with their nationality.