I think there's a little more going on in the story then there may seem to be at first glance.
The school not only has an American flag flying out front, but actually says the pledge of allegiance every day before classes. That is increasingly uncommon in much of the country, but they still do it in this school.
Also, it does not appear that the school's problem is with the flying of a flag, but rather than it has a neutral policy of banning the flying of any large flag or banner in the parking lot.
The reason that is important is that the school may not legally distinguish between what flags or banners are permitted, and which ones aren't. In other words, if they permitted large American flags, they would also have to permit large "pride" flags, large black lives matter flags or banners, or any other politicized, left-wing flag that many of us might find offensive. In other words, the only way to stop that is to have a facially neutral rule limiting the size of any flags that can be flown, including the American flag.
Considering that there's already a large American flag flying in front of the school, and that the school says the pledge of allegiance every morning, I'm inclined to think that this policy was drafted by someone savvy enough about the laws who wanted to ban large politicized left wing flags and banners, and that this policy was the only legal way to do that.
