Let’s look at the difference between I am a closed person and the correct phrase I am a private person.
Czech learners sometimes want to say that they are more reserved or that they prefer to keep things to themselves, and they use the sentence I am closed person. In English, however, this does not work. The adjective closed is not normally used in this way to describe someone’s personality.
If, on the other hand, we want to say that we are reserved, that we do not share everything about ourselves straight away, or that we value our privacy, a much more natural phrase is I am a private person.
W: She is a very closed person and doesn’t talk much.
R: She is a very private person and doesn’t talk much.