When I first began receiving my own DNA matches I was frustrated by the number of trees marked "private." Since that time I have somewhat of a change of heart.
On several occasions I have started public trees solely due to having DNA matches with persons whose ancestors lived in the same geographical areas as my own ancestors but for whom I did not have an actual known connection. I then spent a lot of time going even farther than my matches had gone in researching their own ancestry in the hope of finding the elusive common ancestor. The problem that I encountered was that I started getting inquiries from persons interested in my exploratory trees asking about various individuals. I found myself having to spend a lot of time answering questions about people about whom I was likely not even connected! I have since changed those exploratory trees to "private" for this reason.
Another reason for marking a tree as "private" is when someone is exploring a possible connection due to an adoption situation. I am currently having a person undergo a test who may or may not be related to my family due to an adoption. If the test proves that an actual relationship exists, I may well change that person's "private" tree to "public" but until the relationship is confirmed, I would keep the tree "private" and would continue to do so if that person wanted me to in the future.
Finally, unlike those who feel that their "years of research" entitles them to keep whatever information that they discover close to their vests, I just have a philosophical difference over the issue of sharing information. Whatever information that I discover about an ancestor I freely post on my tree in the hope that it will be shared by others. I seek no credit for it but merely feel that I bringing it to light for the benefit of all who may be interested in it. If I discover that the father of Mary Jones was actually John Jones, why should I wish to keep that information to myself or even be able to claim some sort of ownership over that information? Wouldn't those who actually lived back in those days have known about that relationship? If I discover a will or some other old document, what right do I have to claim ownership of it? How can someone claim ownership of what was supposed to be a public document in most cases? I would freely post it and wouldn't consider it stealing for someone to make use of the document even if it was through my own efforts that the document was located in the first place.