1. What has broken the bond of trust that once existed between parents and teachers?From talking to teacher friends here in Blighty, the worst thing is not that teachers have been boxed into a corner
vis a vis imposing discipline (because only weak teachers have a problem with imposing discipline without using violence or the fear of it; we all know of a little old man or lady who never raised their hand to anyone yet all the kids were scared of crossing) but that - almost across the board, parents side with their kids now in any dispute of their behaviour, rather than siding with the teachers (or indeed with any other adult).
2. Why has it happened?A number of factors have come into play.
Schools themselves have adopted child-centred practices - every kid gets called by their first name, for example, and there are no longer "pupils" (implying passive consumers who have education done to them) or "scholars" (the Victorian term that simply describe someone being at school) but "students" (which, wrongly at all but undergraduate levels and above, implies that the kids are the ones actively pursuing their education. They aren't.)
Media-stoked fear of paedophilia, along with longer working hours and community breakdown, means that one the one hand almost everyone in the neighbourhood is a stranger these days, and that one the other strangers are not to be trusted (not only by kids, which is fair enough, but by other adults too).
And, on top of that, a broad media thrust towards "good parenting" and a trend to smaller family sizes, longer working hours, atomisation of the extended family, and more single parents (the majority of whom still arise through divorce, not irresponsibility) has made most parents worried, deep-down about how good they are at parenting.
So if a teacher tells a parent that little Jimmy is a bully or is disruptive in class, etc., a 1950s, 60s or 70s parent was more likely to side with the teacher and scowl down at the kid, say "you're in big trouble when you get home", etc.
An 80s, 90s and 00s parent is increasingly likely to side with the kid and refuse to believe anything bad anyone says about them, and even punch out the teacher (one of my teacher friends has seen this happen more than once).
This is not limited to teachers; any adult who tells off a kid who isn't theirs is these days subjected to a tirade of abuse from the kid (and probably always was), but runs the risk of the parent finding out and then coming looking for confrontation. And woe betide anyone who raises a child's bad behaviour with the parent - it is usually taken as a slight on their parneting skills.
All of this is not helped by a culture-wide mythologising of childhood - kids are now supposed to be inherently good, angelic things that only do bad things because of some past harm that has been done to them, rather than intrinsically amoral beings that have to be taught, and to learn or themselves, how to behave, the difference between right and wrong, good manners, etc.
And I think that, in turn, stems from the popularisation of Freudian psychology, where people are the puppets of past experience, rather than beings with free will. (Wide ranging enough for you?

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3. What can be done to repair the relationship?Well, it won't be simple, quick or easy, since whole trends in society are at fault, not just one thing.
But I detect hopeful trends - there seem to be the first stirrings of a shift away from endless psychoanalysis and drug treatment towards Cognitive Behaviour Therapy, on the grounds that one tends to help identify the causes of problems without doing much to solve them, while the other is pragmatically focused on solving them without worrying too much about the causes.
If that continues, maybe society will begin to realise that how we treat children needs to shift from treating them with kid gloves as if the most important thing about them is that they need to be protected from things, and towards treating them as beings that need to learn and experience things, and not just in school.
Ultimately, I think the role of schools and parents taken together is not to teach kids what to know, or what to think. Between them, the most important thing is to teach kids
how to think.
For this reason, science, or rather the philosophy and structure of the scientific method, should be as compulsory as English or mathematics, rather than an option like French or geography.