Bear speaks ill of the King because he believes him to be a tyrant. Bear has a rather unique perspective in life because he spent several years as a monastic, training to become a priest. During the Middle Ages in England, society was ordered into the nobility, the peasantry, and the religious monks and priests. The nobility and peasantry had a very direct relationship with one another, where the peasantry labored and produced food in exchange for protection from their Lords. The religious existed in relationship to the nobility and peasantry, but were offered a special point of view and protection as people who negotiated with God. During his time in the monastery, Bear was removed from the context of peasant life and had the opportunity to realize that the noble-peasant relationship was one of exploitation.
You see, peasants never had the choice whether or not to live lives totally in service to their Lords and King. Their entire lives would be spent laboring, starving, and facing severe punishment for very minor crimes. Under the feudal system, everything in the kingdom belonged to the King, even the animals that lived on the land. As Bear mentions, to kill a wild animal is to commit a crime against the King. If they were to be found out, they might suffer a punishment as terrible as having their hand cut off. The laws and social structure of feudal England were set up in such a way that peasants had only the choice to obey or die.
Bear and his compatriots, like John Ball, want to change the social and legal structure of their society. They believe that the peasants of England are exploited and deserve more money, more freedom, and more food in return for their labor. We learn that John Ball is a priest (or at least wears priest's robes) and is offered the luxury of living outside of the exploitative relationship of noble-peasant. Nonetheless, priests served the peasant communities and spent their time among people who did suffer in this society. Bear's friends are plotting a rebellion to restore some power and freedoms to the hands of the people so that they can achieve a good quality of life.