The dispute between Becket and Henry II came to a head in the Constitutions of Clarendon in 1164, which sought to limit the Church's power in England. Becket refused to sign the Constitutions and went into exile in France. He later returned to England but faced opposition from supporters of the king, leading to his assassination in 1170.
The question of who was right in this conflict is a complex one and depends on one's perspective. Becket was a defender of the Church's authority and believed that it should not be subject to the king's interference. Henry II, on the other hand, saw the king as the supreme authority in England and sought to ensure that the Church did not have too much power and influence.
In terms of the historical consequences, Becket's martyrdom elevated his status as a saint and martyr and strengthened the autonomy of the Church. However, the conflict also weakened the relationship between the king and the Church, leading to a period of unrest and tension in England.
Therefore, the question of who was right between Becket and King Henry II is a matter of opinion and depends on one's interpretation of the historical context and the values and principles involved in the conflict.