Some people are happy to have their daily/weekly schedule posted where it can be seen by everyone or by a particular group, and this can be very useful for organizing meetings and such. For some people, having a viewable schedule is even required as part of their job.
I recognize the practicality of a viewable schedule, but I would never voluntarily and routinely post my schedule other than for the short-term purpose of scheduling a meeting or exam within some specified time frame.
Why not? Some of my reasons are somewhat rational, and some are not. The semi-rational reasons relate to the fact that my schedule is a moving target, with meetings, appointments, and urgent tasks appearing daily. I can set aside time for essential commitments as needed, but the apparent blank spaces on my schedule are not really blank and I don't want any more of them filled in than necessary.
My students can find me when they need to -- my door is almost always open when I am in my office -- and students know they can stop by whenever they have questions or topics to discuss. They don't need to see my schedule.
I can't really explain the irrational reasons (by definition?), but I did have a rather formative, early-career experience that may explain some of it.
One day when I was looking for one of my grad students in his office, which was at one end of a lab room, I saw something that looked like this on a chalkboard near his desk:
Monday/DATE
8:27 AM: FSP arrives in office, checks email
8:42 AM: FSP on phone with colleague X
8:55 AM: FSP at computer/typing
9:00-10:00 AM: FSP teaching (SCI123, room 10)
10:00-10:06 AM: FSP outside classroom, answers question from students
10:06-10:09 AM: FSP talks to Z in office, checks mailbox
10:10 AM: back in office, checks email
10:20 AM: FSP goes to library
10:55 AM: FSP returns (not carrying any books)
etc.
My first thought was: OK... so maybe he was trying to find a time when we could meet (????). As far as I knew, we never had trouble finding a time to chat, so I wasn't sure why the detailed accounting was necessary. I asked him about it, and he said he just liked to keep track of things. I decided not to worry about it. I was more worried about the fact that he was making no progress on his research.
I got more worried when a colleague asked me if I knew that this student spent a lot of time just standing outside my office door, out of my sight, apparently listening to my phone conversations and taking notes.
And then this student, some others, and I visited another research lab for a few days. When we were done and I was checking over the car, I saw an unfamiliar notebook and I opened it to see whose it was. It was my student's, and, on the first page, I saw that he had itemized the things in my suitcase. At some point, he had opened my suitcase while we were traveling, and he had written down what was in it.
When I asked him about this, he said that he was very interested in what it was like to be a professor, and he was accumulating as much information as he could, including what I brought on research trips. He also said that I wasn't doing a good job of being a mentor. A good mentor would tell him these things so he didn't have to get the information himself. He did not think he should have to ask. He saw absolutely nothing wrong with going through my suitcase (secretly).
Our adviser-student relationship went downhill fast, and it was all very unpleasant, especially since I was an assistant professor and had not yet established a track record of successfully advising students, sane or otherwise.
This student wanted to know what it was like being a professor: how much time I spent on certain tasks, how I organized my files, what was I doing when I was in my office, how many socks did I bring on research trips etc. He was much less interested in doing research, although being a professor at a university happens to involve quite a lot of research.
You can wear the same pair of socks every day on a research trip if you want, but more important is why you are making that trip, what you do on the trip, and what you take away from the trip. He was not so interested in those aspects of being a professor, and that may explain in part why he never became a professor.
My ex-student wondered: What do professors do with all that time when they weren't in a classroom teaching or in a faculty meeting seething? Although his methods of finding out the answer were disturbing, it's a fair question, and one that lots of people ask.
Yet I think my student realized that carefully documenting my activities still didn't give a complete picture, and thus his methods escalated. I had some suspicions that he was also rummaging around in my computer when I wasn't in the office, probably just to find out what I was doing (and not to steal anything or destroy anything), but even then I think there were still gaps in his knowledge of What Professors Do All Day.
I value the fact that, on at least some days, I have a bit of flexibility in my working hours. I like that I can decide whether to spend a certain 'free' hour preparing for class, meeting with a graduate student, talking with colleagues, or working on a paper.
Perhaps I would be more OK about routinely posting my schedule if (1) none of the people viewing my schedule were bizarre intrusive sneaks; and (2) there were a way to label time in which I am extremely busy, but just not with any particular thing.
Mostly, though, I'd rather just reveal my schedule as necessary to find a time for a meeting or other event. Other than that, I'd prefer to be mysterious, leaving everyone wondering what I'm really doing while I'm glaring at my computer, talking with a colleague in a cafe, or wandering around campus.
By producing papers, proposals/grants, and students, I think I show well what I am doing overall, and that seems like more important information than what I am doing at 3:00 on Wednesday.