If a kid in your school is expelled for getting in trouble, but not on school property, a controversy is likely to ensue over whether that's fair. A controversy is a long discussion in which many people express opposing views.
Controversy means a public dispute in which there is strong disagreement, but the topic can be as unimportant as a new movie. There might be a controversy in the pages of fashion magazines over whether shorter hems are really in style, or whether fashion models should be as thin as they are. Controversy is from Latin contrōversus ""turned in an opposite direction, disputed," from the prefix contrā "against" plus versus, form of vertere "to turn."