"In all my career, it has always been that way." Furthermore, I consider it to be perfectly normal! Here's where I think it's coming from:
"Surrounding the IT operation, there is a business." Sometimes a real business gets to plan, sometimes it has to respond quickly to an opportunity, and sometimes it is required to react. "That's business."
When your boss comes to you with a new urgent request, that request is urgent, and it's probably most-urgent to another stakeholder within the business ... and, it is that business which, ultimately, all of you are tasked to serve. The apparent-cacophony with which these requests sometimes come flying in is, as I just said, "normal!" (After all, you can never truthfully say that the IT business is boring ...)
Therefore, from day to day you will be dealing with competing priorities, "many balls in the air at once," the constant necessity to table work on a project-in-progress to deal with some new fire (or, something that might "close a business deal"), and to be able to do that nimbly.
"Many programmer-types" ... (and I can say this honestly because I [also ...] am *one) ... prefer to have their heads-down on one thing and to concentrate [exclusively] on that one thing. "Well, if that's you right now ... change."
Devise an accurate system whereby you can track the expected and actual progress of all of these requests, and to "simply, report" how the prioritized incoming-request stream inevitably delays each one. The most important thing for you and your management, and for his or her management, and for the various stakeholders that have an interest in everything that you are doing, is simply that "they always know." If they are always timely informed, they can be adaptable, and so can you. Of course it is your manager that primarily bears the responsibility of "dealing with the up-streams," but the timely information with which to do that comes (partially) from you.