A more sensible English translation from Korean would be to use the phrase "in year X" rather than the phrase "X years old": a newborn is in year 1; after 12 months they are in year 2; etc.
In fact, this whole discussion is more about a choice of phrasing rather than the numbers. When indexing arrays, sometimes we're talking about an offset from the first element (starting with "0"), and sometimes we're talking about ordinal element numbers (starting with "first"). Some programming language designers found that offsets are more useful (because that choice tends to simplify the underlying arithmetic), while others found that ordinal numbers are more useful (because the word "first" should mean "1", to simplify communication between people).
In fact, this whole discussion is more about a choice of phrasing rather than the numbers. When indexing arrays, sometimes we're talking about an offset from the first element (starting with "0"), and sometimes we're talking about ordinal element numbers (starting with "first"). Some programming language designers found that offsets are more useful (because that choice tends to simplify the underlying arithmetic), while others found that ordinal numbers are more useful (because the word "first" should mean "1", to simplify communication between people).