She refuses to discuss the reasons for her divorce.
Tips
usage
Carries mild criticism, implying the speaker has something to hide or isn't being fully transparent. Not neutral. Compare with 闭口不谈 (stronger, 'seal one's lips and say nothing').
grammar
Usually takes an object via 对 or 关于: 对...避而不谈 / 关于...避而不谈. Can also appear bare, with the topic implied from context.