Why である instead of でいる？

Question

One solution that I heard is aru can be used for people you're not close to and iru for people you are close to, so like a humble thing, but, I don't know if it's actually said, and aru is for unliving things, but is this really into depth, and I just didn't get into depth? By the way, this isn't a clone, because all the things I have searched up are dumbed down into one meaning but no explanation really... To stay, to keep, but why aru isn't?

Answer 1

As I said in the comment section, you must see the particle before ある/いる. "ある is for inanimate things and いる is for animate things" is a rule that is relevant when ある/いる is used as an existence verb. This rule has nothing to do with the usage of である and でいる because these constructions do not express the existence of something/someone in the first place.

Basically ～である is a stilted copula, i.e., a literary version of ～だ. ～でいる is a copula in progressive aspect, i.e., "to stay/keep X" in English. See: What is the difference between でいる and である in this example? / What is the meaning/grammar behind noun + でいる?

Here is a very simple summary:

• Xがいる。
  There is X.
  _{(X is a person, animal, etc.)}
• Xがある。
  There is X.
  _{(X is an inanimate object.)}
• AはXである。
  A is X. (literary/formal)
  _{(X is a noun, a na-adjective or a no-adjective)}
• AはXでいる。
  A stays X. / A keeps being X.
  _{(X is a noun, a na-adjective or a no-adjective)}

And simplest examples:

• 猫がいる。
  There is a cat.
  _{(猫 is an animal)}
• 本がある。
  There is a book.
  _{(本 is an inanimate object)}
• 私は学生である。
  I am a student.
  _{(である is a stilted だ)}
• 私は元気でいる。
  I am keeping healthy. / I'm doing well.