The protests in Brazil are justified because they are protesting very important issues. The protests started because of an increase in the price of public transportation. This alone is enough reason for a protest because many of the people who use public transportation are poor and cannot afford a price hike.
Brazil, even under a so-called left-wing party and government (the Worker's Party), has become ever so unequal, ever more dominated by major and transnational corporations, and has seen its environment and people more and more degraded and exploited. This is the source of the protests and demonstrations that have rocked Brazil recently.