Boss told me I needed two weeks advance to schedule vacation. Giving a month and a half notice yet still wants to deny me one of the days. Do I just call in sick that day before?

I am planning to take off from September 22-27. This means I’ll be gone Thursday-Friday and Monday-Tuesday. My boss is taking a half day that Friday and said I can’t take that day off although other employees assured him that they would be able to cover for both of us. What should I do? I’d like to just call in sick for the Thursday and Friday. If other employees said they could handle him only there for half the day and me gone, why is it such an issue? I’m giving over a month’s notice!