Translation:Yes, I am American.
The correct answer is "Yes, I'm american". "American person" would sound strange. です (desu) is often used to refer when we talk about ourselves. For exemple, you could say "嬉しい です" (ureshii desu) that means "I'm (feeling) happy", in this case you don't need to say 私 (watashi = me, I).
It likely flagged it for two reasons: "person" and "it."
"It is an American person" is a strange sentence in English. While not technically grammatically incorrect, it also isn't a very natural sentence.
With people, you most often do not use the word "it," and with -an endings for nationalities, it isn't followed with "person."
Japanese is really contextual, and the subject of the sentence is often left out. There's nothing wrong with adding it, and I believe it's nice to include it to be more formal, but it's usually not necessary. In fact, sometimes saying the subject ("anata" meaning "you") can actually be considered rude or offensive.
It's like in English if you asked what i was up to and I replied "Doing the dishes.". It's understood that I'm talking about myself so I don't need to say "I am doing the dishes."
In japanese language textbooks, there's usually pictures or an example conversation so that we can understand the context.
I've been falling back on some sign language I know. Literal translation to spoken word doesn't make much sense.
Same kind of thing, when you go from one language to another, proper translation would be what makes sense in English, not literal.
Japanese seems similar to sign language in that you often describe the subject. So America + person = American.
amerika-jin and the "jin" is the agentive particle. It's almost like saying "America-person". It's what we translate into English as "American": Someone who is from America or has American heritage.
You could say "amerikan desu", but that would strongly mark you as a non-fluent foreign speaker.
In this reading (じん) it’s basically a suffix which you stick to the end of a place and the resulting word means a person from that place. So it’s somewhat similar to the English suffixes “-(i)an, -ese, -ish” (as in “American, Chinese, Turkish), but be careful not to use 日本人 etc. as an adjective, or to speak about the language. It means specifically a person from Japan.
The why is easy to answer. Basically, the Japanese have been on a borrowing spree of Chinese words for the better part of the last 1500 years. In fact in the beginning they would just straight up write Chinese and Japanese itself wasn’t written at all. So during that time, they borrowed a number of words involving 人, including the way of forming a demonym (name for the inhabitants of a place) by adding -人. Since it was borrowed from Chinese, its pronunciation is based on the Chinese one at the time, so it became modern 人.
However Japanese also had a native word for “person” – ひと – which continued to exist. And since it essentially meant the same thing as the Chinese word, they just took the same character to write that word as well. As a result, there are multiple pronunciations for the same character – because it’s essentially two different words but they are written with the same character because they have the same meaning.
Maybe it’s easier to understand if we imagine a similar situation in English. Suppose English had no writing and the only writing system people know is Japanese. Then if we want to write the English word “person”, we’d probably borrow the character 人 from Chinese because it means the same thing. But we also have words directly borrowed from Japanese (“gaijin” 外人 for instance) and obviously we would use the Japanese spelling for those. So both the sound “person” and ”jin” would both be written 人. In fact there may be more. “Android” for example is borrowed from Greek and literally means “man-shaped, man-like”, so we might end up writing that as something like 人形. Then 人 would have a third pronunciation “andro”. This is basically what happened in Japanese.