Managing your priorities implies that because you attach "A1" to something, it will be done first, and is the most important thing to do today. The reality is that a single call from a single person can completely nullify all of the "managed priorities" on your list. Anyone who has received an unexpected call from the ER knows what I mean.
You have priorities, but you can't manage them in the sense that you can't control or determine how they will play out. They change as new information makes its way into your attention. I feel that saying you are "managing your priorities" simply means you are believing you can determine in advance the order you do the things in your day. I feel that "having priorities" is more of a high-level awareness allowing for the constantly shifting nature of the things you have to do.