Protests like these are hardly ever results of careful planning. It usually takes a combination of multiple grievances and time for it fester, until a really explosive brew is form. That explosive brew then needs a spark to ignite it all.
In the case of Brazil, remember that the preparations for the world cup and Olympics began at a time when the country was growing at 7.5% a year, the future looked really bright, and most of the corruption scandals had not been uncovered yet. Over time, major corruption scandals began to appear, the economic growth slowed down dramatically, inflation began to creep up and threaten the recently emerged "new middle class" , the costs for the world cup exploded well above what had been budgeted, and all the promises for better infra-structure failed to materialize (while taxes went up). This created a massive amount of stored discontentment, dormant under the surface of calm, that just need a small spark to explode. And what was that spark? Well, Brazil's presidential election is next year and Dilma's main rival is the governor of the state of Sao Paulo, Geraldo Alckmin. In a move against him, a group affiliated with Dilma's party began to organize a series of protests against the price of the bus fares in the state of Sao Paulo. Unknown to them, that relatively small protest was the spark that ignited the rage of the entire population against Dilma and Lula. That is why the OP was praising the protest during the initial phase, but said that it later it turned into a "right wing coup". The protest was sponsored by the federal government, but they quickly lost control over it and it turned on them. They created the monster, but could not control it.
I hope this answers your question.
