That is completely false and part of the black legend. The spaniards didn't kill millions of amerindians. About 99% of the deaths were caused by small pox and other european diseases to which amerindians were not prepared.
If I had counted diseases I would have said tens or hundreds of millions. Amerindian tribes were more or less equal with one another regarding imported European diseases. Yet, in the Caribbean, the region first colonised by the Spaniards, 99% of the indigenous population disappeared, a much higher rate than the death accountable to diseases in the Aztec or Inca empires. This is because most Caribbean Indians were used as slave labour to build the early colonial infrastructure. Many more were massacred for fun or because they didn't want to convert or to become subjects of the King of Spain.
Father Bartolomé de las Casas, the “Defender of the Indians” estimated there were 6 million Taíno and Arawak in the Caribbean at the time of Columbus's arrival in 1492. Nowadays, the Caribbean population is mostly of African descent with some European blood, and only barely discernible traces of Native American DNA on some islands. In comparison, countries like Mexico or Bolivia, who also suffered heavily from diseases, have retained a majority of Native American genes today, because they were numerous and advanced enough to withstand the excesses of the conquistadors.
But even where whole populations were not exterminated in a short time frame, Amerindians suffered immensely from the Spanish exploitation. It's not because large Amerindians populations survived in Central America and in the Andes that millions of people didn't die their from Spanish hands, whips and guns (as opposed to diseases). Slave labour of native populations was used intensively by Spanish colonisers, for example in the silver mines of the Andes. At Potosi (Bolivia) alone, one of the biggest silver mines in the world, Henry Hobhouse mentions in his remarkable book
Seeds of Change (page 337) that '
between 1560 and 1620, about ten thousands Amerindians died each year, or 600,000 in sixty years. This number excludes children and people killed by European diseases, but includes working children over eight.'
Hobhouse doesn't mention the death rate afterwards. However, Potosi was exploited by the Spaniards until the war of independence of Bolivia in the early 1800's. It is likely that the cumulated total of deaths during those 250 years exceeds one million people, perhaps even two millions. These deaths are less obvious because they are spread out over a very long time and those are indirect casualties from exhaustion, excessive whipping or the occasional shot. They are nevertheless deaths on the Spanish conscience.
Potosi is just one examples among many on a huge continent. It would be unreasonable to deny that millions of Amerindians were killed by the Spaniards during the 300 years of colonisation. Knowing the fanatical religiosity of the Spaniards at the time, it is easy to conceive how violent forced conversions could lead to widespread sporadic massacres all over the continent. When I see the tortures and executions committed on fellow Christians and Europeans by the Spaniards in the Low Countries, it is hard to imagine how they would have behaved in a more civilised manner with people that they referred to as "savages".
I think you should read a lot more and not trust what the Spanish education system wants you to believe about your country's history. It's so common for national governments to hide the ugly part of their past that it is almost stereotypical. Japanese schools don't teach about the massacres committed by the Japanese Imperial army in Korea, China and South-East Asia before and during WWII. Belgians don't learn about Leopold II's massacres in Congo at school. French schools happily skip over the Algerian War of Independence. I don't expect Spaniards to be taught all this at school.