This creates a great deal of uncertainty on the part of staff, who need to mesh their own plans and thinking with that of their leader. For those who work for a secretive leader it is a most frustrating experience. In fact, it usually ends badly for the leader or their staff because a lack of transparency leads to conflict. If I don't know what is in the mind of my leader, I will either have to beg for forgiveness when I get it wrong or lead with caution in case I cross an invisible line I cannot see. It is one of the most discourteous behaviors a supervisor can exhibit.
What is the psychology behind a lack of transparency in a leader's thinking? First, consider that information is power! If I have information others don't have I have power that they don't have and frankly some leaders want that power. It also allows a leader to share information selectively with those they deem worthy of having it and withhold it from those they don't. If it sounds like a mind game, it pretty much is.
Second, if I as the leader have all access to information and others don't I can play people or departments against one another. FDR famously did this in his leadership style, and while he achieved great things, it was at the expense of the relationships of his senior leaders who were told what he wanted them to know (and different leaders were told different things). Only he had access to all the information and, therefore, the keys to the kingdom. Others had to figure it out themselves, often at the expense of conflict with others. There is certainly an element of manipulation here.
Third, secrecy allows a leader to keep staff on edge as they present "surprises" in terms of decisions that staff have no context for. Again, this smacks of selfish and problematic behavior. Never would they want their staff to surprise them—ever—but they have no compulsion to surprise their staff. They are the leaders, after all. This also means that they have different standards for themselves than for others.
This behavior is unfair, deeply dysfunctional, unempowering, and foolish. It usually masks a leader's deep insecurity. It is a form of control that allows the leader to keep the initiative and ensure that others don't have it. What is amazing to me is that boards allow this kind of behavior to take place.
There are things a leader does not share for valid reasons, but secretive leaders create problems for those around them - whatever their motivation. No healthy leader withholds critical information from their staff and/or board. If they do, it eventually comes back to bite them or the organization.