Not in the sense of owing him an explanation, but in the decent sense of giving him feedback so he can improve.
After all, the candidate took time and trouble - it is a kindness.
An application to YC is unlike an interview; with an interview you usually know what your weakness was, or what the interviewer's hangup was.
If you consider this to be "entitlement-thinking", then does not your thinking seem arrogant?
Actually, your thinking is a sign of weakness. When the candidate is stronger than you, or your decision was flippant, then you dont want to run the risk of being proven wrong or bested. So you choose the easy way out.