I just hate to see an opportunity for learning missed, whether I am the student or teacher. I would also like to evaluate whether there is a fundamental problem they perceive, large or small, or if it is an issue of communication. And if they do see a valid major flaw, I sure would love to know about it.
Perhaps, as can be inferred from their "it's not you, it's me" breakup-esque language, they are concerned about causing damage by providing rejection feedback. Perhaps they are concerned they don't have sufficient time to evaluate applications thoroughly enough to provide reliably meaningful feedback. Or perhaps they are concerned that their feedback might be taken more strongly than intended. Perhaps in reality it is more beneficial overall for them NOT to provide feedback. But given a choice, I would opt for feedback and believe I would benefit from it.