If I had to hazard a guess based on the things they say and write, I would say their hate is based on their inability to accept the Reformed teachings such as predestination, eternal security, the Calvinist TULIP, and the Doctrines of Grace. Since they cannot accept these doctrines, and cannot refute them biblically, they instead turn to Calvin himself and do their best to vilify him. Presumably, they believe that by vilifying Calvin, they are automatically refuting everything he taught.
The primary tool used by the anti-Calvinist crowd to vilify Calvin, is the execution of Michael Servetus in 1553. Servetus was a Spanish theologian and physician whose theology can best be described as a smorgasbord of heresy. In examining his writings, it becomes clear that Servetus embraced some Arianism, Sabellianism, Humanism, Monophysitism, Panentheism, Unitarianism, Dualism, and Gnosticism. Although he didn't subscribe fully to each of these heresies, he did hold to aspects of them. The culmination of his heretical beliefs, however, was his denial of the biblical Trinity, the virgin birth, and the Deity of Jesus Christ; and these served to embroil Servetus in what became a deadly controversy.
Although many believe that Servetus was simply an innocent man who happened to disagree with Calvin and paid the ultimate price for his refusal to accept Calvinism; history refutes this belief. Servetus had been publishing his beliefs for some time before the Roman Catholic church decided to stop him. In 1552 he was arrested by the Roman Catholic church, and sentenced to death for his heretical teachings. This was during the Spanish Inquisition. Before he could executed, however, Servetus escaped, and began to travel through Europe. The French Inquisition also tried him for heresy and sentenced him to death, but were forced to burn him in effigy due to his escape from prison in Vienna.
It is important to remember the time period in which all of this took place. The Roman Catholic church not only exerted great influential power throughout much the known world, but actually ruled in many parts of it. This was also during the beginning of the Protestant Reformation, and there were some areas which were ruled according to Protestant beliefs. Such was the case in Geneva, Switzerland, where Servetus eventually turned up.
Although Servetus had not planned to stay in Geneva, and was on his way to Italy, while in Geneva he was recognized and arrested on August 13, 1553. There is speculation that it was Calvin himself who recognized Servetus and requested he be arrested. Whether or not this is true, I do not know; however, if true, Calvin had good reason to have Servetus arrested, as the man posed a significant threat to the spiritual well-being of Calvin's flock, particularly those who were not well versed in biblical theology, were immature in their faith, and susceptible to the heresies taught by false teachers such as Michael Servetus.
A week after his arrest, the authorities wrote to Vienna asking for information on the charges against Servetus. The response of the Viennese authorities was to demand he be extradited back to Vienna for execution. The Genevan city council gave Servetus a choice: either stay in Geneva and face trial, or be sent back to Vienna and face execution. Although Servetus was well aware that Calvin was in Geneva, he was also aware Calvin held no political power there, and that the city council was full of Calvin's enemies. Therefore, thinking there was a possibility of exoneration, Servetus begged to stay in Geneva.
Contrary to the conspiratorial beliefs held by the anti-Calvin people, John Calvin did not rule over Geneva during this period. The only place where he might have been able to exert any influence was in the Church Consistory. However, in the case of Michael Servetus, the Consistory was completely bypassed, and the case went straight to the Council of the 200, a governing City Council comprised of 200 Genevan citizens. It would have been impossible for Calvin to have any influence in this Council, as he was not a citizen of Geneva, and would not be for another six years. Additionally, those on the Council were, by and large, opposed to Calvin and his teachings. He had no influence on the Council, he had no authority in Geneva to arrest, torture or execute anyone, much less Michael Servetus. The Genevan authorities had effectively prevented Calvin and his followers from exerting any influence on the case.
During his trial, Servetus did not offer much of a defense, and instead chose to use his time reviling Calvin, probably because the majority of the Council were Calvin's enemies, and Servetus likely thought he actions would put him in their good graces. John Calvin's only real role in the entire case, was to appear as an expert witness for the state, to provide testimony of Servetus' heresy. This he did.
Once it was clear that Servetus was a heretic, the Genevan council realized the only two choices they had were to either banish him or execute him. Swiss law at the time allowed for execution in cases of heresy, and the Genevan authorities wrote to the councils in Berne, Zurich, Schaffhausen and Basle, asking for their advice in the Servetus matter. Each one of them wrote back advising Servetus be executed. To the Genevan Council, their decision became clear to them, and they chose to execute him by burning him at the stake. It is known that Calvin visited Servetus in prison, praying for him, praying with him, and pleading with Servetus to renounce his heresy and thus save his life. Servetus refused. He believed that he was an emissary of the Christ, and that he was to usher in the return of Christ within the next 20 or 30 years. Because of these beliefs, Servetus believed he would not be executed. When it became clear that he was going to die, Calvin pleaded with the authorities to employ a more humane and virtually painless method of execution – beheading – rather than being burned alive. The authorities refused, and Servetus was burned alive at the stake on October 26, 1553.
Myths Surrounding the Servetus Incident
Myth #1: John Calvin was a cold-blooded murderer who executed dozens and dozens of people during his tyrannical reign in Geneva.
Fact: Michael Servetus was executed by the Genevan authorities, and Calvin had no influence over their decision to do so. Furthermore, Servetus was the only individual put to death for heresy in Geneva during Calvin's lifetime. It should also be remembered that Calvin was not even a citizen of Geneva when Servetus was executed, and therefore had no legal right to even hold public office, nor even pastor a church unless there were no Genevan's with the expertise to hold a pastorship. It is also important to note that Servetus himself not only believe heretics should be executed, but actively called for the execution of John Calvin.
Myth #2: Calvin wrote a letter claiming responsibility for Servetus' death.
Fact: John Calvin wrote a letter to William Farel, dated February 13, 1546, wherein he wrote, “Servetus wrote to me a short time ago, and sent a huge volume of his dreamings and pompous triflings with his letter. I was to find among them wonderful things, and such as I had never before seen; and if I wished, he would himself come. But I am by no means inclined to be responsible for him; and if he come, I will never allow him, supposing my influence worth anything, to depart alive.” A poor choice of words to be sure, but hardly a confession of guilt. Furthermore, Calvin knew he had no influence over the Council, and he knew that only the Council had the authority to put someone to death. The letter Calvin received from Servetus was little more than Servetus mocking and reviling Calvin. Therefore, Calvin's statements can best be understood as a frustrated and angry man lashing out against someone who has wronged him.
Myth #3: Calvin wanted Servetus dead, and watched the execution with a sinister smile on his face.
Fact: There is no evidence whatsoever that Calvin attended Servetus' execution. Furthermore, it is well known that Calvin visited Servetus in prison, prayed for him, prayed with him, and begged Servetus to recant and thus be saved. Hardly the actions of someone wanted Servetus dead.
Myth #4: Calvin was a tyrant who ruled Geneva with an iron fist.
Fact: Calvin was not even a resident of Geneva, and as a legal alien in the city, he was prohibited from holding any legal office. Furthermore, the City Council was largely opposed to Calvin, and remained so until his death. In 1538, Calvin was asked to leave Geneva, and he happily did so, moving to Strasbourg where he pastored a church there until 1541. At that time Geneva called him back to pastor the Genevan church that had been experiencing some problems. Calvin returned, but reluctantly so. He was hardly a tyrant, and he never ruled in Geneva or anywhere else.
Myth #5: Calvin executed dozens and dozens of people who disagreed with him.
Fact: Michael Servetus was the only person executed for heresy in Geneva during Calvin's lifetime, and he was executed by the Genevan Council, not by John Calvin.
“Was Geneva a Theocracy?” by Michael Horton
“John Calvin’s Geneva” by W. J. Grier
“Theology of Michael Servetus” by Christopher W. Myers
“Calvin vs. Servetus” by J. Steven Wilkins
Schaff's Church History (Good background on the incident)
Schaff's chapter on Servetus