First, tolerance - or, as it would then be termed, liberty of conscience- was not a common thing for the 17th century European religious mind to like. People tended to think in terms of correct belief, and error. There was also no secular/sacred division, like we have today. Any religious dissent would in turn create quarrels among the leadership, which could threaten to split and break up the very fragile newly-established Bay colony .

Calvinists believed that an omnipotent God already knew who was going to be damned and saved. But how could you tell if you were one or the other? Certainly, you would be going to the correct church, be obedient to he commandments, but this simply acting good ( "works") was not enough. Puritans would often therefore spend great amounts of time keeping and reviewing their diaries, trying to tell if God was showing favor to them. There was a constant tension between trying very hard to do the Godly thing, or simply assuming that, since God had already decided, there was nothing to be done.

So, when Hutchinson began to argue that it was possible for someone to tell if they were in the Elect, that the Holy Ghost would be within them and grant them a revelation, it was a very big claim. More dangerously, she said these people could also tell if OTHER people were of the Elect. And, naturally, if ministers in the Colony did not agree with this, they were unfit to preach. And of course, by implication, any leaders of the Colony were unfit to lead, as well...This split the Colony into two hostile camps by 1637. Wheelwright at one point said that true believers must hew down those who did not agree : " must kill them with the worde of the Lorde", and though he was speaking figuratively, it was only a matter of time before he and then Hutchinson were brought to trial, examined, and banished.

Good, classic summary of this and other conflicts is The Puritan Dilemma, by Edmund S Morgan

To a large degree, the Antinomian controversy hinged on the question of where religious authority comes from.

The leaders of the Massachusetts Bay colony explicitly were trying to erect a Bible Commonwealth in the New World - that is, they were trying to establish a society in which law and morality would be based on holy scripture. The divines who led the colony felt it was their duty to watch over their neighbours - in John Winthrop's words, the colony was to be "knit together in this work as one man" - and this meant they would need to enforce religious orthodoxy through the courts and government.

Winthrop and other Puritan leaders were "preparationists" - meaning that they believed salvation could only come through God's grace, but they also thought unregenerate individuals (i.e., people who were not yet saved) could prepare themselves to receive this grace through a contemplation or their sins. This meant that civil authorities had an important role to play in controlling the religious climate; heterodox ideas could undermine the cause of salvation.

Hutchinson and Wheelwright differed in that they were not preparationists - instead, they believed that God's grace was offered freely, and was intuited through revelation (a vision or a feeling) rather than studied through scripture. In other words, salvation came directly from God, and did not require the interpretation of scripture by Puritan divines.

So the "covenant of grace" was dangerous for a couple of reasons: (1) it challenged the religious orthodoxy of the colony, which its leaders were at pains to maintain, (2) it placed religious authority in the conscience of individuals rather than in the scriptural knowledge of Puritan divines.

Hutchinson made matters worse by insulting the magistrates and threatening a curse upon the colony, which ultimately led them to banish her for sedition. But it was her religious ideas that threatened the ideological basis of the colony.

Roger Williams took things even further, questioning the right of civil authorities to legislate religious matters at all - which led him to establish a policy of religious tolerance in Rhode Island.