In terms of events that "break" social norms and how people will react to them, each circumstance is different.
For example, allowing cell phones in restaurant, when it began, was a break with the social norm. Most people would go out to dinner to relax and enjoy a meal cooked away from home, and often the companionship of friends. Loud and rowdy drunks were frowned upon, as were screaming children and rude and/or obnoxious groups of people...generally in a nice restaurant (as opposed to a fast-food place). However, now people bring their cell phones with them. The phones may ring continuously or conversation may be so loud that it makes it difficult to enjoy your meal. I have seen and heard about different reactions. Some people ask to be moved to another location; some people will leave the restaurant and not order dinner. Sometimes, people find the behavior so unbearable that they say something to the other diner.
Another situation we have seen are the no-smoking laws that have been enforced across the country. This has been very difficult for smokers, who may have tried to quit or find smoking relaxing. For those of us who do not smoke, it is a relief, but it creates a struggle on the part of smokers. Some smokers have reacted with anger and frustration.
If you are looking for a potential problem within society, tell a nation that guns are no longer legal, or abortions are banned. The uprising would be fierce and furious. People feel very strongly about some things. The nation is already divided on these two issues, but changing the laws to favor one stance over another would result in wide-spread protest, and perhaps even violence.
Looking to the past and our country's decision to make slavery illegal ripped the country apart and caused a war: it needed to be done, but it divided not only the nation, but families as well. When young men started to be drafted into the Vietnam War, there were nationwide protests, young men and/or their families moved to Canada to avoid going to war, and the nation was divided as to the necessity and the ethical reasoning to become involved in that particular "war." This, too, destroyed families and turned the public against the government.
All of these examples provide instances of broken social norms. I believe that you could write a paragraph about any of them, if you have knowledge of the difficulty (some background/research) so that you can support your position with specific examples to promote your viewpoint.
You may want to write a persuasive essay, if your teacher wants you to convince him or her, or an informational essay which reports the facts. See the links provided for more information to these kinds of writings for essays.