When are professors most free during a semester?
The end of the semester particularly the period between the end of lectures and when students finally leave campus (which may be well after you've submitted grades) can be the busiest part of the semester because that's when you spend a lot of time dealing individually with students that have questions, complaints, or problems.  The reason that this is so time consuming is that there are typically lots of these students, and each complaining student can easily take an hour out of your day.    

Meanwhile you may also be grading a lot of term papers or student projects and you're also busy writing, proctoring, and grading final exams.