The monarchy never started to push the end of slavery. One of Pedro II's daughters did, but Pedro II himself never did.
Have you ever read anything about the life of Pedro II beside what is on Internet? He personally supported and started several measures to begin the end of slavery, many times even knowing that it would damage his prestige among the slaveholders. He personally supported Eusebio de Queiroz when the Conservative government decided to end the slave trade. Again he supported Nabuco de Araújo when he decided several actions against landowners and politicians of Pernambuco involved in illegal arrivals of slaves in 1855. He always refused to give nobility titles to families that were involved in the slave trade. Heck, among all the "Coffee Barons" of Rio de Janeiro there isn't a single one from the Breves family, the greates slaveholders of the province.
When the American Civil War ended in 1864 he asked to his ministers to create laws that would start the end of slavery through a "Law of the Free Womb" - that would give freedom to all slaves that would be born after the signature of the law. Two years later he personally wrote a letter to the "Committee for the Abolition of Slavery" stating that emancipation would be the highest priority of government as soon as the war in Paraguay would be over. Such letter was received by indignation in the Parliament, and he received a public answer in the newspapers by senator José de Alencar - at the time was the most read Brazilian writer - who accused Pedro II of "giving attention to European philanthropists instead of defending the national interests".
After that, for three years he tried to include the issue of the end of slavery in the annual "Speech from the Throne", but the government didn't let him do it. After the war was over he pressure Parliament to approve the law, and he needed to change three times the president of Parliament before he could find one who would accept to bring the law to a vote (it would five, but two of the names appointed by him simply refused to get the mission).
Meanwhile the slaveholders of Minas Gerais, São Paulo and Rio de Janeiro forgot all their political divisions and founded the Club of Farming and Commerce to defend their interests in the Court. Who was their representantive to the press? Cristiano Ottoni, the brother of Teofilo Ottoni, the most die-hard Republican politician in the Empire. It alone shows how they were more commited with the defense of slavery than the defense of monarchy.
Before the final vote Pedro was being extremely criticized in the press for making such "horrible law" because he wanted to have a good impression in Europe instead of being concerned with national problems, was called a despot and of being too involved in politics. It was finnally approved in 1871 by 61 to 35 after intense political pression and briberies, and the damage to his public image was so intense that he didn't pressure for new legislation regarding slavery until 1884.
So, saying that he was never started to push for the end of slavery is simply wrong. He was the one who started the political process to have it approved 24 years before 1888. And in retribution for this he gained several damages in his reputation and in the image of monarchy among those who until then were his most loyal allies.