It's what someone does when they don't want to talk about something. It might mean John does things like changes the subject, or goes quiet, or starts giving one-word answers. That sort of thing.
January 19, 2017
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"closes up" means that he becomes silent and withdrawn. He doesn't answer the question and becomes slightly uncomfortable. Another expression is "he just shuts down." It means the same thing. :)
January 19, 2017
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