King George III viewed the American colonial rebellion as a threat that could lead other parts of the British Empire to also seek independence. The concern was that success of the Thirteen Colonies in gaining independence might encourage similar aspirations in other territories, potentially destabilizing the empire.
King George III perceived the struggle with the American colonies as a considerable risk to the stability of the entire British Empire. The fear was that if the Thirteen Colonies successfully formed their own independent nation, it could inspire and embolden other parts of the empire to seek the same independence.
The correct answer to the student's query is that other parts of the empire might also try to break away if the colonies proved successful in their bid for independence. This concern was valid, considering the far-reaching British Empire and the disparate regions under its control, which were closely watching the events unfolding in North America.
The intensive twenty-year period which started with the war in 1754 saw increasing strife between Great Britain and her American colonies. Policies that effectively changed the status quo, such as salutary neglect giving way to tighter control and new taxes, fueled the colonial protest and desire for self-governance.
After their significant contributions to the British victories in the French and Indian War, the colonists had expected greater autonomy and access to new lands, but instead faced even more restraints which only intensified their dissatisfaction with British rule.