You can say “I’m not sharing that” and still be a good friend.

Closeness is not measured in disclosure. Holding something back is not a judgment on the friendship, and a good friend can usually accept that a subject is closed without needing to know why. The reflex to explain comes from a fear of seeming cold. A plain answer, kindly given, does the job better than a long one.

Have a line ready that does not slam the door, something along the lines of preferring not to get into it. Use it once, then ask them something, so the conversation keeps moving.