It's pretty well understood by people far less experienced than the CEO (i.e. me) that you need to split those messages up.
Empathy is unconditional. It says "wow, that must be really painful/terrible/scary". It carries no judgement around the accuracy of such feelings, only an understanding that they are real for the other person.
Disagreeing comes later after you have shown there are legitimate competing solutions.
"I'm sorry you feel that way" fails at the first so you haven't yet earned the right to disagree agreeably.
What makes it complicated, though, is that some people interpret "I'm sorry" as an admission of guilt or agreement, so conservative lawyers and others recommend specifying what you feel sorry for so as to not give away the farm.
Empathy is unconditional. It says "wow, that must be really painful/terrible/scary". It carries no judgement around the accuracy of such feelings, only an understanding that they are real for the other person.
Disagreeing comes later after you have shown there are legitimate competing solutions.
"I'm sorry you feel that way" fails at the first so you haven't yet earned the right to disagree agreeably.