To me, "poner en evidencia" also has the connotation of embarrassing the person you are doing this to. For example:
Ella me puso en evidencia en frente de todos.
She embarrassed me in front of everyone (by sharing some secret about me).
So here's my translation:
poner en evidencia a alguien = to divulge a piece of detrimental information about someone with the intent of embarrassing them
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If you find something wrong with my Spanish, please correct it!
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