Minimum days or Early dismissal days or half days exist because states require teachers to have a minimum number of professional development hours in order to renew their teaching certification. In AZ, we have to renew every 6 years and have 300 PD hours.
I don't know the legality of teachers acquiring those hours on our own or within our districts, but I do know that evidence for such things was always random as hell. Some would electronically let the state know you had 6 hours on a certain date and others would literally print out a 'proof of PD' on colored paper. Imagine collecting several dozen of those over 6 years and if you lose them, you're out of a job.
Anyway, as a teacher, we hate these days. It means we either smash 6-7 hours of instruction into 4 or more commonly, drop everything but reading and math that day. The kids go home and we spend all afternoon doing district-chosen professional development. Because we have to get those hours. Not because it makes us better teachers.
Scheduling these days was all over the place, initially. Some did it on Fridays, others on Monday mornings. The most common is Wednesdays.
As for hating parents, districts just schedule things to screw the fewest number of people. As someone with a mainstream student and a special needs student at a separate school, yeah, you're often going to be in the minority side that isn't getting a convenient schedule. But 5 angry parents is better than 500, any way you slice it.
As for teachers and parents, we hate shitty parents. Not the busy ones, not the ones who wish they had more time for their kid....the shitty ones who are actively bad for their child. Theyre mostly ghosts anyway. The parents we need to see most - we never see. The ones we want to communicate with consistently - all of the phone numbers in the system are disconnected. We don't like the parents that undo all the good we do every time their child goes home.
And we hate PD. It's busy work. We'd rather have a consistent schedule and just teach.