This thread is just a disaster, it's so meaningless.
I'm sure this thread has at least a few different views of what you mean by "humiliation", and the more extreme side is clearly going to be denied into oblivion, while minor humiliation (Like "don't pick your nose, that's [nasty/disgusting/dirty/whatever]" to a child in a queue at the supermarket) is acceptable. Why? Because it's a choice the parent has to make, do you stop them doing something WHEN THEY'RE DOING IT or do you tell them it was wrong in private. It's public humiliation but the awful wording in this thread probably has people thinking about much more dramatic examples (I can't provide you with an example now because I actually can't imagine the type of humiliation someone would want to put their child through)
As an aside, however, humility is a good trait to have from your child, and in the case of having a super arrogant, probably law-breaking child a lesson in humility is important. Think about all those videos that have some angry guy doing something stupid like trying to intimidate a black-belt in kick-yo-ass-fu (heh heh Mr T fool pun). Public humiliation that we can [almost] all laugh at and consider valid.
Besides - where are you all drawing the line at for children? Are teenagers children or adults? Or teenagers? If they're not children, when is a teenager not a child, 13? I never considered myself a teenager until I was 15.
TL
R "Humiliation" is a very broad term and this thread woefully underexplains the scenario. Too many variables for me to make this as a serious discussion thread rather than a "Absolve yourself of something you may feel is wrong, however vaguely"