My boss wants me to "check in" before leaving work. Is this fair?

I work from 9–5:30 and, more often than not, stay late when I need to get something done. Of course, this being the US, overtime is not given, but I am glad to volunteer my time for the good of the company and for my coworkers.

However, my boss has now requested that I “check in” before leaving to check and see if there is anything left I can help out with.

I personally find this unfair – after 5:30, my work time ends and my personal time begins. Some days I may have an appointment, an errand, a class, a meeting with a friend or family member, or (if I’m lucky!), a date. This idea that my workload can not be planned out before the last second seems almost absurd to me. I feel like forcing me to say to my managers face “no, I can not help with this right now, but I can tomorrow” puts me in a position where I am being viewed in a negative light as an employee.

My question is not whether I should find a new company to work at, or whether this is normal behavior for a company to engage in. My question is: Am I wrong to think this is completely unfair, and overall bad management tactics? Or am I being bratty thinking I am entitled to a life outside of work?