Why should we use a private constructor?

Assuming you mean an instance method inside the Day class, it could certainly take a Parcel as a parameter like you said. But where would the Parcel data be assigned? And how would that method even be invoked in the first place? To invoke it we'd have to already have an instance of Day, and that means we'd probably have already set all of its fields!

We want to make a new instance of Day using data from the Parcel object, so that's why it's in a constructor, not an instance method. Why private? Because generally you want to strive to give the least amount of access necessary to any data within the code you write. In the Day class, it looks like Ben only intended the static Creator<Day> object instance to use that constructor, so he limited the constructor's access to private. He could've made it public, but that would raise the questions: where outside the Day class is it being used, and why does it need to be used there? At this point in the project it didn't need to be used anywhere else, so it wasn't enabled to be used elsewhere.