From Longman Dictionary of Contemporary Englishtouchy subject/question etctouchy subject/question etcDIFFICULTa subject etc that needs to be dealt with very carefully, especially because it may offend people SYN sensitive Asking about a reporter’s sources can be a touchy business. → touchy
Examples from the Corpus
touchy subject/question etc• He also knew the answers to some touchy questions.• Morris's lasting influence is a touchy subject at the White House.• You know money is a touchy subject with me. 