Yes. Teachers should have the ability to take a personal day if it is required. Although teachers should be present in their classroom, they undoubtedly have issues that arise during the course of the school year where personal time could be utilized. I think they make a huge commitment to our children, and they deserve a little bit of discretionary paid time off.
Teachers are not any different than other people. They have lives. They occassionally need to go to the doctor, or take their car into the shop, do whatever else they need to do. A limited amount of personal days every year is reasonable to ensure that teachers can have a proper work-life balance and it should not present any harm to our children's education.